Big Data User's Guide For S-P 8: The Knowledge To Act

the knowledge to act™
Big Data User’s Guide

®
for S-PLUS 8
May 2007
Insightful Corporation
Seattle, Washington
Proprietary Insightful Corporation owns both this software program and its
Notice documentation. Both the program and documentation are
copyrighted with all rights reserved by Insightful Corporation.
The correct bibliographical reference for this document is as follows:
®
Big Data User’s Guide for S-PLUS 8, Insightful Corporation, Seattle,
WA.
Printed in the United States.
Copyright Notice Copyright © 1987-2007, Insightful Corporation. All rights reserved.

Insightful Corporation
1700 Westlake Avenue N, Suite 500
Seattle, WA 98109-3044
USA
ii
ACKNOWLEDGMENTS
S-PLUS would not exist without the pioneering research of the Bell
Labs S team at AT&T (now Lucent Technologies): John Chambers,
Richard A. Becker (now at AT&T Laboratories), Allan R. Wilks (now
at AT&T Laboratories), Duncan Temple Lang, and their colleagues in
the statistics research departments at Lucent: William S. Cleveland,
Trevor Hastie (now at Stanford University), Linda Clark, Anne
Freeny, Eric Grosse, David James, José Pinheiro, Daryl Pregibon, and
Ming Shyu.
Insightful Corporation thanks the following individuals for their
contributions to this and earlier releases of S-PLUS: Douglas M. Bates,
Leo Breiman, Dan Carr, Steve Dubnoff, Don Edwards, Jerome
Friedman, Kevin Goodman, Perry Haaland, David Hardesty, Frank
Harrell, Richard Heiberger, Mia Hubert, Richard Jones, Jennifer
Lasecki, W.Q. Meeker, Adrian Raftery, Brian Ripley, Peter
Rousseeuw, J.D. Spurrier, Anja Struyf, Terry Therneau, Rob
Tibshirani, Katrien Van Driessen, William Venables, and Judy Zeh.
iii
S-PLUS BOOKS
®
The S-PLUS documentation includes books to address your focus
and knowledge level. Review the following table to help you choose
the S-PLUS book that meets your needs. These books are available in
PDF format in the following locations:
• In your S-PLUS installation directory (SHOME\help on
Windows, SHOME/doc on UNIX/Linux).
• In the S-PLUS Workbench, from the Help 䉴 S-PLUS
Manuals menu item.
® ®
• In Microsoft Windows , in the S-PLUS GUI, from the
Help 䉴 Online Manuals menu item.
S-PLUS documentation.
Information you need if you... See the...
Are new to the S language and the S-PLUS GUI, Getting Started
and you want an introduction to importing data, Guide
producing simple graphs, applying statistical
®
models, and viewing data in Microsoft Excel .
Are a system administrator or a licensed user and S-PLUS licensing Web

you need guidance licensing your copy of S-PLUS site
and/or any S-PLUS module. keys.insightful.com/
Are a new S-PLUS user and need how to use User’s Guide
S-PLUS, primarily through the GUI.
Are familiar with the S language and S-PLUS, and S-PLUS Workbench
you want to use the S-PLUS plug-in, or User’s Guide
customization, of the Eclipse Integrated
Development Environment (IDE).
Have used the S language and S-PLUS, and you Programmer’s Guide
want to know how to write, debug, and program
functions from the Commands window.
iv
S-PLUS documentation. (Continued)
Information you need if you... See the...
Are familiar with the S language and S-PLUS, and Application

you want to extend its functionality in your own Developer’s Guide
application or within S-PLUS.
Are familiar with the S language and S-PLUS, and Guide to Graphics
you are looking for information about creating or
editing graphics, either from a Commands
window or the Windows GUI, or using S-PLUS-
supported graphics devices.
Are familiar with the S language and S-PLUS, and Big Data
you want to use the Big Data library to import and User’s Guide
manipulate very large data sets.
Want to download or create S-PLUS packages for Guide to Packages

submission to the Comprehensive S Archival
Network (CSAN) site, and need to know the steps.
Are looking for categorized information about Function Guide

individual S-PLUS functions.
If you are familiar with the S language and S-PLUS, Guide to Statistics,
and you need a reference for the range of statistical Vol. 1
modelling and analysis techniques in S-PLUS.
Volume 1 includes information on specifying
models in S-PLUS, on probability, on estimation
and inference, on regression and smoothing, and
on analysis of variance.
If you are familiar with the S language and S-PLUS, Guide to Statistics,
and you need a reference for the range of statistical Vol. 2
modelling and analysis techniques in S-PLUS.
Volume 2 includes information on multivariate
techniques, time series analysis, survival analysis,
resampling techniques, and mathematical
computing in S-PLUS.
v
vi
CONTENTS
S-PLUS Books iv
Chapter 1 Introduction to the Big Data Library 1

Introduction 2
Working with a Large Data Set 3
Size Considerations 7
The Big Data Library Architecture 8
Chapter 2 Census Data Example 21

Introduction 22
Exploratory Analysis 25
Data Manipulation 37
More Graphics 41
Clustering 45
Modeling Group Membership 53
Chapter 3 Creating Graphical Displays

of Large Data Sets 61
Introduction 62
Overview of Graph Functions 63
Example Graphs 69
vii
Contents
Chapter 4 Advanced Programming Information 105

Introduction 106
Big Data Block Size Issues 107
Big Data String and Factor Issues 113
Storing and Retrieving Large S Objects 119
Increasing Efficiency 121
Appendix: Big Data Library Functions 123

Introduction 124
Big Data Library Functions 125
Index 161
viii
INTRODUCTION TO THE BIG
DATA LIBRARY
1
Introduction 2
Working with a Large Data Set 3
Finding a Solution 3
No 64-Bit Solution 5
Size Considerations 7
Summary 7
The Big Data Library Architecture 8
Block-based Computations 8
Data Types 11
Classes 14
Functions 15
Summary 19
1
Chapter 1 Introduction to the Big Data Library
INTRODUCTION
In this chapter, we discuss the history of the S language and large data
sets and describe improvements that the Big Data library presents.
This chapter discusses data set size considerations, including when to
use the Big Data library. The chapter also describes in further detail
the Big Data library architecture: its data objects, classes, functions,
and advanced operations.
To use the Big Data library, you must load it as you would any other
library provided with S-PLUS: that is, at the command prompt, type
library(bigdata).
• To ensure that the library is always loaded on startup, add

library(bigdata) to your SHOME/local/S.init file.
®
• Alternatively, in the S-PLUS GUI for Microsoft Windows ,
you can set this option in the General Settings dialog box.
• In the S-PLUS Workbench, you can set this option in the
S-PLUS section of the Preferences dialog box, available from
the Window menu.
2
Working with a Large Data Set
WORKING WITH A LARGE DATA SET

When it was first developed, the S programming language was
designed to hold and manipulate data in memory. Historically, this
design made sense; it provided faster and more efficient calculations
and modeling by not requiring the user’s program to access
information stored on the hard drive. Data size has outstripped the
rate at which RAM size increased; consequently, S program users
could have encountered an error similar to the following:
Problem in read.table: Unable to obtain requested dynamic

memory.
This error occurs because S-PLUS requires the operating system to

provide a block of memory large enough to contain the contents of
the data file, and the operating system responds that not enough
memory is available.
While S-PLUS can access data contained in virtual memory, the
maximum size of data files depends on the amount of virtual memory
available to S-PLUS, which depends in turn on the user’s hardware
and operating system. In typical environments, virtual memory limits
your data file size, and then it returns an out-of-memory error.
Finally, you can also encounter an out-of-memory error after
successfully reading in a large data object, because many S functions
require one or more temporary copies of the source data in RAM for
certain manipulation or analysis functions.
Finding a S programmers with large data sets have historically dealt with
Solution memory limitations in a variety of ways. Some opted to use other
applications, and some divided their data into “digestible” batches,
and then recompile the results. For S programmers who like the
flexibility and elegant syntax of the S language and the support
provided to owners of an S-PLUS license, the option to analyze and
model large data sets in S has been a long-awaited enhancement.
Out-of-Memory The Big Data library provides this enhancement by processing large
Processing data sets using scalable algorithms and data streaming. Instead of
loading the contents of a large data file into memory, S-PLUS creates a
special binary cache file of the data on the user’s hard disk, and then
3
refers to the cache file on disk. This out-of-memory design requires

relatively small amounts of RAM, regardless of the total size of the
data.
Scalable Although the large data set is stored on the hard drive, the scalable
Algorithms algorithms of the Big Data library are designed to optimize access to
the data, reading from disk a minimum number of times. Many
techniques require a single pass through the data, and the data is read
from the disk in blocks, not randomly, to minimize disk access times.
These scalable algorithms are described in more detail in the section
The Big Data Library Architecture on page 8.
Data Streaming S-PLUS operates on the data binary cache file directly, using
“streaming” techniques, where data flows through the application
rather than being processed all at once in memory. The cache file is
processed on a row-by-row basis, meaning that only a small part of
the data is stored in RAM at any one time. It is this out-of-memory
data processing technique that enables S-PLUS to process data sets
hundreds of megabytes, or even gigabytes, in size without requiring
large quantities of RAM.
Data Type S-PLUS provides the large data frame, an object of class bdFrame. A
big data frame object is similar in function to standard S-PLUS data
frames, except its data is stored in a cache file on disk, rather than in
RAM. The bdFrame object is essentially a reference to that external
file: While you can create a bdFrame object that represents an
extremely large data set, the bdFrame object itself requires very little
RAM.
For more information on bdFrame, see the section Data Frames on
page 11.
S-PLUS also provides time date (bdTimeDate), time span (bdTimeSpan),
and series (bdSeries, bdSignalSeries, and bdTimeSeries) support for
large data sets. For more information, see the section Time Date
Creation on page 157 in the Appendix.
Flexibility The Big Data library provides reading, manipulating, and analyzing
capability for large data sets using the familiar S programming
language. Because most existing data frame methods work in the
same way with bdFrame objects as they do with data.frame objects,
the style of programming is familiar to S-PLUS programmers. Much
existing code from previous versions of S-PLUS runs without
4
Working with a Large Data Set
modification in the Big Data library, and only minor modifications

are needed to take advantage of the big-data capabilities of the
pipeline engine.
Balancing While accessing data on disk (rather than in RAM) allows for scalable
Scalability with statistical computing, some compromises are inevitable. The most
Performance obvious of these is computation speed. The Big Data library provides
scalable algorithms that are designed to minimize disk access, and
therefore provide optimal performance with out-of-memory data sets.
This makes S-PLUS a reliable workhorse for processing very large
amounts of data. When your data is small enough for traditional
S-PLUS, it’s best to remember that in-memory processes are faster
than out-of-memory processes.
If your data set size is not extremely large, all of the S-PLUS traditional
in-memory algorithms remain available, so you need not compromise
speed and flexibility for scalability when it's not needed.
Metadata To optimize performance, S-PLUS stores certain calculated statistics as

metadata with each column of a bdFrame object and updates the
metadata every time the data changes. These statistics include the
following:
• Column mean (for numeric columns).
• Column maximum and minimum (for numeric and date
columns).
• Number of missing values in the column.
• Frequency counts for each level in a categorical column.
Requesting the value of any of these statistics (or a value derived from
them) is essentially a free operation on a bdFrame object. Instead of
processing the data set, S-PLUS just returns the precomputed statistic.
As a result, calculations on columns of bdFrame objects such as the
following examples are practically instantaneous, regardless of the
data set size. For example:
• mean(census.data$Income)
• range(census.data$Age)
No 64-Bit Are out-of-memory data analysis techniques still necessary in the 64-
Solution bit age? While 64-bit operating systems allow access to greater
amounts of *virtual* memory, it is the amount of *physical* memory
5
that is the primary determinant of efficient operation on large data

sets. For this reason, the out-of-memory techniques described above
are still required to analyze truly large data sets.
64-bit systems increase the amount of memory that the system can
address. This can help in-memory algorithms handle larger problems,
provided that all of the data can be in physical memory. If the data
and the algorithm require virtual memory, page-swapping (that is,
accessing the data in virtual memory on the disk) can have a severe
impact on performance.
With data sets now in the multiple gigabyte range, out-of-memory
techniques are essential. Even on 64-bit systems, out-of-memory
techniques can dramatically outperform in-memory techniques when
the data set exceeds the available physical RAM.
6
Size Considerations
SIZE CONSIDERATIONS
While the Big Data library imposes no predetermined limit for the
number of rows allowed in a big data object or the number of
elements in a big data vector, your computer’s hard drive must
contain enough space to hold the data set and create the data cache.
Given sufficient disk space, the big data object can be created and
processed by any scalable function.
The speed of most Big Data library operations is proportional to the
number of rows in the data set: if the number of rows doubles, then
the processing time also doubles.
The amount of RAM in a machine imposes a predetermined limit on
the number of columns allowed in a big data object, because column
information is stored in the data set’s metadata. This limit is in the
tens of thousands of columns. If you have a data set with a large
number of columns, remember that some operations (especially
statistical modeling functions) increase at a greater than linear rate as
the number of columns increases. Doubling the number of columns
can have a much greater effect than doubling the processing time.
This is important to remember if processing time is an issue.
Summary By bringing together flexible programming and big-data capability,

S-PLUS is a data analysis environment that provides both rapid
prototyping of analytic applications and a scalable production engine
capable of handling datasets hundreds of megabytes, or even
gigabytes, in size.
In the next section, we provide an overview to the Big Data library
architecture, including data types, functions, and naming
conventions.
7
THE BIG DATA LIBRARY ARCHITECTURE

The Big Data library is a separate library from the S-PLUS engine
library. It is designed so that you can work with large data objects the
same way you work with existing S-PLUS objects, such as data frames
and vectors.
Block-based Data sets that are much larger than the system memory are
Computations manipulated by processing one “block” of data at a time. That is, if
the data is too large to fit in RAM, then the data will be broken into
multiple data sets and the function will be applied to each of the data
sets. As an example, a 1,000,000 row by 10 column data set of double
values is 76MB in size, so it could be handled as a single data set on a
machine with 256MB RAM. If the data set was 10,000,000 rows by
100 columns, it would be 7.4GB in size and would have to be handled
as multiple blocks.
Table 1.1 lists a few of the optional arguments for the function
bd.options that you can use to set limits for caching and for
warnings:
Table 1.1: bd.options block-based computation arguments.
bd.option argument Description
block.size The block size (in number of rows), the number

of bytes in the cache to be converted to a
data.frame.
max.convert.bytes The maximum size (in bytes) of the big data

cache that can be converted to a data.frame.
max.block.mb The maximum number of megabytes used for

block processing buffers. If the specified block
size requires too much space, the number of rows
is reduced so that the entire buffer is smaller than
this size. This prevents unexpected out-of-
memory errors when processing wide data with
many columns. The default value is 10.
8
The Big Data Library Architecture
The function bd.options contains other optional arguments for

controlling column string width, display parameters, factor level
limits, and overflow warnings. See its help topic for more
information.
The Big Data library also contains functions that you can use to
control block-based computations. These include the functions in
Table 1.2. For more information and examples showing how to use
these functions, see their help topics.
Table 1.2: Block-based computation functions.
Function name Description
bd.aggregate Use bd.aggregate to divide a data object into

blocks according to the values of one or more of
its columns, and then apply aggregation
functions to columns within each block.
bd.aggregate takes two required arguments:
data, which is the input data set, and by.columns,
which identifies the names or numbers of
columns defining how the input data is divided
into blocks.
Optional arguments include columns, which
identifies the names or numbers of columns to
be summarized, and methods, which is a vector
of summary methods to be calculated for
columns. See the help topic for bd.aggregate for
a list of the summary methods you can specify
for methods.
bd.block.apply Run an S-PLUS script on blocks of data, with

options for reading multiple input datasets and
generating multiple output data sets, and
processing blocks in different orders. See the
help topic for bd.block.apply for a discussion on
processing multiple data blocks.
bd.by.group Apply the specified S-PLUS function to multiple

data blocks within the input dataset.
9
Table 1.2: Block-based computation functions. (Continued)
bd.by.window Apply the specified S-PLUS function to multiple

data blocks defined by a moving window over
the input dataset. Each data block is converted to
a data.frame, and passed to the specified
function. If one of the data blocks is too large to
fit in memory, an error occurs.
bd.split.by.group Divide a dataset into multiple data blocks, and

return a list of these data blocks.
bd.split.by.window Divide a dataset into multiple data blocks

defined by a moving window over the dataset,
and return a list of these data blocks.
For a detailed discussion on advanced topics, such as block size issues

and increasing efficiency, see Chapter 4, Advanced Programming
Information.
10
Data Types S-PLUS provides the following data types, described in more detail
below:
Table 1.3: New data types and data names for S-PLUS.
Big Data class Data type
bdFrame Data frame
bdVector, bdCharacter, bdFactor, Vector

bdLogical, bdNumeric, bdTimeDate,
bdTimeSpan
bdLM, bdGLM, bdPrincomp, bdCluster Models
bdSeries, bdTimeSeries, bdSignalSeries Series
Data Frames The main object to contain your large data set is the big data frame,
an object of class bdFrame. Most methods commonly used for a
data.frame are also available for a bdFrame. Big data frame objects
are similar to standard S-PLUS data frames, except in the following
ways:
• A bdFrame object stores its data on disk, while a data.frame
object stores its data in RAM. As a result, a bdFrame object has
a much smaller memory footprint than a data.frame object.
• A bdFrame object does not have row labels, as a data.frame
object does. While this means that you cannot refer to the
rows of a bdFrame object using character row labels, this
design reduces storage requirements and improves
performance by eliminating the need to maintain unique row
labels.
• A bdFrame object can contain columns of only types double,
character, factor, timeDate, timeSpan or logical. No other
column types (such as matrix objects or user-defined classes)
are allowed. By limiting the allowed column types, S-PLUS
ensures that the binary cache file representing the data is as
compact as possible and can be efficiently accessed.
11
• The print function works differently on a bdFrame object than

it does for a data frame. It displays only the first few rows and
columns of data instead of the entire data set. This design
prevents accidentally generating thousands of pages of output
when you display a bdFrame object at the command line.
Note
You can specify the numbers of rows and columns to print using the bd.options function. See
bd.options in the S-PLUS Language Reference for more information.
• The summary function works differently on a bdFrame object

than it does for a data frame. It calculates an abbreviated set
of summary statistics for numeric columns. This design is for
efficiency reasons: summary displays only statistics that are
precalculated for each column in the big data object, making
summary an extremely fast function, even when called on a
very large data set.
Vectors The S-PLUS Big Data library also introduces bdVector and six
subclasses, which represent new vector types to support very long
vectors. Like a bdFrame object, the big vector object stores data out-of-
memory as a cache file on disk, so you can create very long big vector
objects without needing a lot of RAM.
You can extract an individual column from a bdFrame object (using
the $ operator) to create a large vector object. Alternatively, you can
generate a large vector using the functions listed in Table A.3 in the
Appendix. Like bdFrame objects, the actual data is stored out of
memory as a cache file on disk, so you can create very long big vector
objects without worrying about fitting them into RAM. You can use
standard vector operations, such as selections and mathematical
operations, on these data types. For example, you can create new
columns in your data set, as follows:
census.data$adjusted.income <- log(census.data$income -

census.data$tax)
Models S-PLUS Big Data library provides scalable modeling algorithms to

process big data objects using out-of-memory techniques. With these
modeling algorithms, you can create and evaluate statistical models
on very large data sets.
12
A model object is available for each of the following statistical

analysis model types.
Table 1.4: Big Data library model objects.
Model Type Model Object
Linear regression bdLm
Generalized linear models bdGlm
Clustering bdCluster
Principal Components Analysis bdPrincomp
When you perform statistical analysis on a large data set with the Big
Data library, you can use familiar S-PLUS modeling functions and
syntax, but you supply a bdFrame object as the data argument, instead
of a data frame. This forces out-of-memory algorithms to be used,
rather than the traditional in-memory algorithms.
When you apply the modeling function lm to a bdFrame object, it
produces a model object of class bdLm. You can apply the standard
predict, summary, plot, residuals, coef, formula, anova, and fitted
methods to these new model objects.
For more information on statistical modeling, see Chapter 2, Census
Data Example.
Series Objects The standard S-PLUS library contains a series object, with two
subclasses: timeSeries and signalSeries. The series object contain:
• A data component that is typically a data frame.
• A positions component that is a timeDate or timeSequence
object (timeSeries), or a bdNumeric or numericSeries object
(signalSeries).
• A units component that is a character vector with
information on the units used in the data columns.
13
The Big Data library equivalent is a bdSeries object with two

subclasses: bdTimeSeries and bdSignalSeries. They contain:
• A data component that is a bdFrame.
• A positions component that is a bdTimeDate object
(bdTimeSeries), or bdNumeric object (bdSignalSeries).
• A units component that is a character vector.
For more information about using large time series objects and their
classes, see the section Time Classes on page 17.
Classes The Big Data library follows the same object-oriented design as the
standard S-PLUS Sv4 design. For a review of object-oriented
programming concepts, see Chapter 8, Object-Oriented
Programming in S-PLUS in the Programmer’s Guide.
Each object has a class that defines methods that act on the object.
The library is extensible; you can add your own objects and classes,
and you can write your own methods.
The following classes are defined in the Big Data library. For more
information about each of these classes, see their individual help
topics.
Table 1.5: Big Data classes.
Class(es) Description
bdFrame Big data frame
bdLm, bdGlm, bdCluster, bdPrincomp Rich model objects
bdVector Big data vector
bdCharacter, bdFactor, bdLogical, Vector type subclasses

bdNumeric, bdTimeDate,
bdTimeSpan
bdTimeSeries, bdSignalSeries Series objects
14
Functions In addition to the standard S-PLUS functions that are available to call
on large data sets, the Big Data library includes functions specific to
big data objects. These functions include the following.
• Big vector generating functions
• Data exploration and manipulation functions.
• Traditional and Trellis graphics functions.
• Modeling functions.
The functions for these general tasks are listed in the Appendix.
Data Import and Two of the most frequent tasks using S-PLUS are importing and
Export exporting data. The functions are described in Table A.1 in
Appendix. You can perform these tasks from the Commands
window, from the Console view in the S-PLUS Workbench, or from
the S-PLUS import and export dialog boxes in the S-PLUS GUI. For
more information about importing large data sets, see the section
Data Import on page 25 in Chapter 2, Census Data Example.
Big Vector To generate a vector for a large data set, call one of the S-PLUS
Generation functions described in Table A.3 in the Appendix. When you set the
bigdata flag to TRUE, the standard S-PLUS functions generate a
bdVector object of the specified type. For example:
# sample of size 2000000 with mean 10*0.5 = 5

rbinom(2000000, 10, 0.5, bigdata = T)
Data Exploration After you import your data into S-PLUS and create the appropriate
Functions objects, you can use the functions described in Table A.4 in the
Appendix. to compare, correlate, crosstabulate, and examine
univariate computations.
Data After you import and examine your data in S-PLUS, you can use the
Manipulation data manipulation functions to append, filter, and clean the data. For
Functions an overview of these functions, see Table A.5 in the Appendix. For a
more in-depth discussion of these functions, see the section Data
Manipulation on page 37 in Chapter 2, Census Data Example.
Graph Functions The Big Data library supports graphing large data sets intelligently,
using the following techniques to manage many thousands or millions
of data points:
15
• Hexagonal binning. (That is, functions that create one point

per observation in standard S-PLUS create a hexagonal
binning plot when applied to a big data object.)
• Plot-specific summarizing. (That is, functions that are based
on data summaries in standard S-PLUS compute the required
summaries from a big data object.)
• Preprocessing data, using table, tapply, loess, or aggregate.
• Preprocessing using interp or hist2d.
Note
The Windows GUI editable graphics do not support big data objects. To use these graphics,
create a data frame containing either all of the data or a sample of the data.
For a more detailed discussion of graph functions available in the Big

Data library, see Chapter 3, Creating Graphical Displays of Large
Data Sets.
Modeling Algorithms for large data sets are available for the following statistical
Functions modeling types:
• Linear regression.
• Generalized linear regression.
• Clustering.
• Principal components.
See the section Models on page 12 for more information about the
modeling objects.
If the data argument for a modeling function is a big data object, then
S-PLUS calls the corresponding big data modeling function. The
modeling function returns an object with the appropriate class, such
as bdLm.
See Table A.12 in the Appendix for a list of the modeling functions
that return a model object.
See Tables A.10 through A.13 in the Appendix for lists of the
functions available for large data set modeling. See the S-PLUS
Language Reference for more information about these functions.
16
Formula operators
The Big Data library supports using the formula operators+, -, *, :,
%in%, and /.
Time Classes The following classes support time operations in the Big Data library.
See the Appendix for more information.
Table 1.6: Time classes.
Class name Comment
bdSignalSeries A bdSignalSeries object from

positions and data
bdTimeDate A bdVector class
bdTimeSeries See the section Time Series

Operations for more information.
bdTimeSpan A bdVector class
Time Series Time series operations are available through the bdTimeSeries class
Operations and its related functions. The bdTimeSeries class supports the same
methods as the standard S-PLUS library’s timeSeries class. See the
S-PLUS Language Reference for more information about these classes.
Time and Date • When you create a time object using timeSeq, and you set the
Operations bigdata argument to TRUE, then a bdTimeDate object is
created.
• When you create a time object using timeDate or
timeCalendar, and any of the arguments are big data objects,
then a bdTimeDate object is created.
See Table A.14 in the Appendix.
Note
bdTimeDate always assumes the time as Greenwich Mean Time (GMT); however, S-PLUS stores
no time zone with an object. You can convert to a time zone with timeZoneConvert, or specify the
zone in the bdTimeDate constructor.
17
Time Conversion To convert time and date values, apply the standard S-PLUS time
Operations conversion operations to the bdTimeDate object, as listed in Table
A.14 in the Appendix.
Matrix The Big Data library does not contain separate equivalents to matrix
Operations and data.frame.
S-PLUS matrix operations are available for bdFrame objects:
• matrix algebra ( +, -, /, *, !, &, |, >, <, ==, !=, <=, =>, %%, %/%)
• matrix multiplication (%*%)
• Crossproduct (crossprod)
In algebraic operations, the operators require the big data objects to
have appropriately-corresponding dimensions. Rows or columns are
not automatically replicated.
Basic algebra
You can perform addition, subtraction, multiplication, division,
logical (!, &, and |), and comparison (>, <, =, !=, <=, >=) operations
between:
• A scalar and a bdFrame.
• Two bdFrames of the same dimension.
• A bdFrame and a single-row bdFrame with the same number of
columns.
• A bdFrame and a single-column bdFrame with the same
number of rows.
The library also offers support for element-wise +, -, *, /, and matrix
multiplication (%*%).
Matrix multiplication is available for two bdFrames with the
appropriate dimensions.
Cross Product Function

When applied against two bdFrames, the cross product function,
crossprod, returns a bdFrame that is the cross product of the given
bdFrames. That is, it returns the matrix product of the transpose of the
first bdFrame with the second.
18
Summary In this section, we’ve provided an overview to the Big Data library
architecture, including the new data types, classes, and functions that
support managing large data sets. For more detailed information and
lists of functions that are included in the Big Data library, see the
Appendix: Big Data Library Functions.
In the next chapter, we provide examples for working with data sets
using the types, classes, and functions described in this chapter.
19
20
CENSUS DATA EXAMPLE
2
Introduction 22
Problem Description 22
Data Description 22
Exploratory Analysis 25
Data Import 25
Data Preparation 27
Tabular Summaries 31
Graphics 32
Data Manipulation 37
Stacking 37
Variable Creation 38
Factors 40
More Graphics 41
Clustering 45
Data Preparation 45
K-Means Clustering 46
Analyzing the Results 47
Modeling Group Membership 53
Building a Model 57
Summarizing the Fit 58
Characterizing the Group 58
21
Chapter 2 Census Data Example
INTRODUCTION
Census data provides a rich context for exploratory data analysis and
the application of both unsupervised (e.g., clustering) and supervised
(e.g., regression) statistical learning models. Furthermore the data sets
(in their unaggragated state) are quite large. The US Census 2000
estimates the total US population at over 281 million people. In its
raw form, the data set (which includes demographic variables such as
age, gender, location, income and education) is huge. For this
example, we focus on a subset of the US Census data that allows us to
demonstrate principles of working with large data on a data set that
we have included in the product.
Problem Census data has many uses. One of interest to the US government
Description and many commercial enterprises is geographical distribution of sub
populations and their characteristics. In this initial example, we look
for distinct geographical groups based on age, gender and housing
information (data that is easy to obtain in a survey), and then
characterize them by modeling the group structure as a function of
much harder-to-obtain demographics such as income, education,
race, and family structure.
Data The data for this example is included with S-PLUS and is part of the
Description US Census 2000 Summary File 3 (SF3). SF3 consists of 813 detailed
tables of Census 2000 social, economic, and housing characteristics
compiled from a sample of approximately 19 million housing units
(about 1 in 6 households) that received the Census 2000 long-form
questionnaire. The levels of aggregation for SF3 data is depicted in
Figure 2.1.
The data for this example is the summary table aggregated by Zip
Code Tabulation Areas (ZCTA5) depicted as the left-most branch of the
schematic in Figure 2.1.
The following site provides download access to many additional SF3
summary tables:
http://www.census.gov/Press-Release/www/2002/sumfile3.html
22
Introduction
Figure 2.1: US Census 2000 data grouping hierarchy schematic with implied
aggregation levels. The data used in this example comes from the Zip Code Tabulation
Area (ZCTA) depicted at the far left side of the schematic.
The variables included in the census data set are listed in Table 2.1.
They include the zip code, latitude and longitude for each zip code
region, and population counts. Population counts include the total
population for the region and a breakdown of the population by
gender and age group: Counts of males and females for ages 0 - 5, 5 -
10, ..., 80 - 85, and 85 or older.
23
Table 2.1: Variable descriptions for the census data example.
New Variable
Variable(s) Name(s) Description
ZCAT5 zipcode five-number zip code
INTPT.LAT lat Interpolated latitude
INTPT.LON long Interpolated longitude
P008001 popTotal Total population
M.00 - M.85 male.00 - Male population by age group:

male.85 0 - 4 years, 5 - 9 years, and so
on.
F.00 - F.85 female.00 - Female population by age

female.85 group: 0 - 4 years, 5 - 9 years,
and so on.
H007001 housingTotal Total housing units
H007002 own Owner occupied
H007003 rent Renter occupied
A script file can be downloaded from Insightful’s Support site that

contains all the commands used in this chapter:
www.insightful.com/support/downloads/examples/
new.census.demo.ssc
If you want to build the cluster model starting on page 57, you also
need to download the following object:
www.insightful.com/support/downloads/examples/
censusDemogr.sdd
Then run data.restore("C:/test/censusDemogr.sdd") to restore it
for use in S-PLUS, where C:/test is an example download folder.
24
Exploratory Analysis
EXPLORATORY ANALYSIS
Data Import The data is provided as a comma-separated text file ( .csv format).
The file is located in the SHOME location (by default your
installation directory) in /samples/bigdata/census/census.csv.
As mentioned on the previous page, you can also download an
analysis script named new.census.demo.ssc to execute the
commands referenced in this chapter.
Reading big data is identical to what you are familiar with in previous
versions of S-PLUS with one exception: an additional argument to
specify that the data object created is stored as a big data (bd) object.
> census <- importData(paste(getenv("SHOME"),
"/samples/bigdata/census/census.csv", sep=""),
stringsAsFactors=F, bigdata=T)
View the data with the Data Viewer as follows:

> bd.data.viewer(census)
The Data Viewer is an efficient interface to the data. It works on big

out-of-memory data frames (such as census) and on in-memory data
frames.
25
Figure 2.2: Viewing big data objects is done with the Data Viewer.
The Data View page (Figure 2.2) of the Data Viewer lists all rows
and all variables in a scrollable window plus summary information at
the bottom, including the number of rows, the number of columns,
and a count of the number of different types of variables (for
example, a numeric, factor). From the summary information, we see
that census has 33,178 rows.
In addition to the Data View page, the Data Viewer contains tabs
with summary information for numeric, factor, character, and date
variables. These summary tabs provide quick access to minimums,
maximums, means, standard deviations, and missing value counts for
numeric variables and levels, level counts, and missing value counts
for factor variables.
26
Figure 2.3: The Numeric summary page of the Data Viewer provides quick access
to minimum, maximum, mean, standard deviation, and missing value count for
numeric data.
Data Before beginning any data preparation, start by making the names
Preparation more intuitive using the names assignment expression:
> names(census) <- c("zipcode", "lat", "long", "popTotal",
paste("male", seq(0, 85, by = 5), sep = "."),
paste("female", seq(0, 85, by = 5), sep = "."),
"housingTotal", "own", "rent")
27
The row names are shown in Table 2.1, along with the original
names.
Note
The S-PLUS expression paste("male", seq(0, 85, by = 5), sep = ".") creates a sequence of 18
variable names starting with male.0 and ending with male.85. The call to seq generates a
sequence of integers from 0 to 85 incremented by 5, and the call to paste pastes together the
string “male” with the sequence of integers separated with a period (.).
A summary of the data now is:

> summary(census)
zipcode lat long
Length: 33178 Min.:17962234 Min.:-176636755
Class: Mean:38830389 Mean: -91084343
Mode:character Max.:71299525 Max.: -65292575
popTotal male.0 male.5

Min.: 0.000 Min.: 0.0000 Min.: 0.000
Mean: 8596.977 Mean: 298.5727 Mean: 322.822
Max.:144024.000 Max.:6247.0000 Max.:6115.000
.
.
.
From summary of the census data, you might notice a couple of

problems:
1. The population total (popTotal) has some zero values,
implying that some zip codes regions contain no population.
2. The zip codes are stored as character strings which is odd
because they are defined as five-digit numbers.
To remove the zero-population zip codes you can do it the you
typically would when working with data frames:
> census <- census[census[, "popTotal"] > 0, ]
However, there is a more efficient way. Notice that the example

above (finding rows with non-zero population counts) implies two
passes through the data. The first pass extracts the popTotal column
and compares it (row by row) with the value of zero. The second pass
28
removes the bad popTotal rows. If your data is very large, using
subscripting and nested function calls can result in a prohibitively
lengthy execution time.
A more efficient “big data” way to remove rows with no population is
to use the bd.filter.rows function available in the Big Data library
in S-PLUS. bd.filter.rows has two required arguments:
1. data: the big data object to be filtered.
2. expr: an expression to evaluate. By default, the expression
must be valid, based on the rules of the row-oriented
Expression Language. For more details on the expression
language, see the help file for ExpressionLanguage.
Note
If you are familiar with the S-PLUS language, the Excel formula language, or another
programming language, you will find the row-oriented Expression Language natural and easy to
use. An expression is a combination of constants, operators, function calls, and references to
columns that returns a single value when evaluated
For our example, the expression is simply popTotal > 0, which you
pass as a character string to bd.filter.rows. The more efficient way
to filter the rows is:
> census <- bd.filter.rows(census, expr= "popTotal > 0")
29
Using the row-oriented Expression Language with bd.filter.rows

results in only one pass through the data, so the computation time will
usually be reduced to about half the execution time of the previously-
described S-PLUS expression. Table 2.2 displays additional examples
of row-oriented expressions.
Table 2.2: Some examples of the row-oriented Expression Language.
Expression Description
age > 40 & gender == “F” All rows with females greater than
40 years of age.
Test != “Failed” All rows where Test is not equal to

“Failed”.
Date > 6/30/04 All rows with Date later than

6/30/04.
voter == “Dem” | voter == “Ind” All rows where voter is either

democrat or independent.
Now, remove the cases with bad zip codes by using the regular
expression function, regexpr, to find the row indices of zip codes that
have only numeric characters:
> census <- bd.filter.rows(census,

"regexpr('^[0-9]+$', zipcode)>0",
row.language=F)
Notes
• The call to the regexpr function finds all zip codes that have only integer characters in
them. The regular expression “^[0-9]+$” produces a search for strings that contain only
the characters 0, 1, 2, ..., 9. The ^ character indicates starting at the beginning of
the string, the $ character indicates continuing to the end of the string and the + symbol
implies any number of characters from the set {0, 1, 2,..., 9}.
• The call to bd.filter.rows specified the optional argument, row.language=F. This
argument produces the effect of using the standard S-PLUS expression language, rather
than the row-oriented Expression Language designed for row operations on big data.
30
Tabular Generate the basic tabular summary of variables in the census data
Summaries set with a call to the summary function, the same as for in-memory data
frames. The call to summary is quite fast, even for very large data sets,
because the summary information is computed and stored internally
at the time the object is created.
> summary(census)
zipcode lat long
Length: 32165 Min.:17964529 Min.:-176636755
Class: Mean:38847016 Mean: -91103295
Mode:character Max.:71299525 Max.: -65292575
popTotal male.0 male.5

Min.: 1.000 Min.: 0.0000 Min.: 0.0000
Mean: 8867.729 Mean: 307.9759 Mean: 332.9889
Max.:144024.000 Max.:6247.0000 Max.:6115.0000
.
.
.
female.85 housingTotal own
Min.: 0.00000 Min.: 0.000 Min.: 0.000
Mean: 92.77398 Mean: 3318.558 Mean: 2199.168
Max.:2906.00000 Max.:61541.000 Max.:35446.000
rent
Min.: 0.000
Mean: 1119.391
Max.:40424.000
To check the class of objects contained in a big data data frame (class
bdFrame), call sapply, which applies a specified function to all the
columns of the bdFrame.
> sapply(census, class)
zipcode lat long popTotal
"bdCharacter" "bdNumeric" "bdNumeric" "bdNumeric"
male.0 male.5 male.10 male.15

"bdNumeric" "bdNumeric" "bdNumeric" "bdNumeric"
.
.
.
31
Generate age distribution tables with the same operations you use for
in-memory data. Multiply column means by 100 to convert to a
percentage scale and round the output to one significant digit:
> ageDist <-
colMeans(census[, 5:40] / census[, "popTotal"]) * 100
> round(matrix(ageDist,
nrow = 2,
byrow = T,
dimnames = list(c("Male", "Female"),
seq(0, 85, by=5))), 1)
numeric matrix: 2 rows, 18 columns.
0 5 10 15 20 25 30 35 40 45 50 55
Male 3.2 3.6 3.8 3.8 2.9 2.9 3.2 3.9 4.1 3.8 3.3 2.7
Female 3.0 3.4 3.6 3.4 2.7 2.8 3.2 3.9 4.0 3.7 3.3 2.7
60 65 70 75 80 85
Male 2.3 2.0 1.7 1.3 0.8 0.5
Female 2.3 2.1 2.0 1.7 1.2 1.1
Graphics You can plot the columns of a bdFrame in the same manner as you do
for regular (in-memory) data frames:
> hist(census$popTotal)
will produce a histogram of total population counts for all zip codes.
Figure 2.4 displays the result.
32
20000
15000
10000
5000
0
0 50000 100000 150000
census$popTotal
Figure 2.4: Histogram of total population counts for all zip codes.
You can get fancier. In fact, in general, the Trellis graphics in S-PLUS
work on big data. For example, the median number of rental units
over all zip codes is 193:
> median(census$rent)
[1] 193
You would expect that, if the number of rental units is high (typical of
cities), the population would likewise be high. We can check this
expectation with a simple Trellis boxplot:
> bwplot(rent > 193 ~ log(popTotal), data = census)
Figure 2.5 displays the resulting graph.
33
TRUE
rent > 193
FALSE
0 2 4 6 8 10 12
log(popTotal)
Figure 2.5: Boxplots of the log of popTotal for the number of rental units above and
below the median, showing higher populations in areas with more rental units.
You can address the question of population size relative to the

number of rental units in a more general way by examining a
scatterplot of popTotal vs. rent. Call the Trellis function xyplot for
this. Take logs (after adding 0.5 to eliminate zeros) of each of the
variables to rescale the data so the relationship is more exposed:
> xyplot(log(popTotal) ~ log(rent + 0.5), data = census)
The resulting plot is displayed in Figure 2.6.
Note
The default scatterplot for big data is a hexbin scatterplot. The color shading of the hexagonal
“points” indicate the number of observations in that region of the graph. For the darkest shaded
hexagon in the center of the graph, over 800 zip codes are represented, as indicated by the
legend on the right side of the graph.
34
12 800
700
10
600
8
log(popTotal) 500
6
400
4 300
200
100
0
1
0 2 4 6 8 10
log(rent + 0.5)
Figure 2.6: This hexbin scatterplot of log(popTotal) vs. log(rent+0.5)

shows population sizes increasing with the increasing number of rental units.
The result displayed in Figure 2.6 is not surprising; however, it

demonstrates the straightforward use of known functions on big data
objects. This example continues with Trellis graphics with
conditioning in the following sections.
The age distribution table created in the section Tabular Summaries
on page 31 produces the plot shown in Figure 2.7:
> bars <- barplot(rbind(ageDist[1:18], -ageDist [19:36]),
horiz=T)
> mtext(c("Female", "Male"), side = 1, line = 3, cex = 1.5,
at = c(-2, 2))
> axis(2, at = bars, labels = seq(0, 85, by = 5),
ticks =F)
35
Note
In creating this plot, the example starts with big out-of-memory data (census) and ends
with small in-memory summary data (ageDist) without having to do anything special to
transition between the two. S-PLUS takes care of the data management.
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
-4 -2 0 2 4
Female Male
Figure 2.7: Age distribution by gender estimated by US Census 2000.
36
Data Manipulation
DATA MANIPULATION
The census data contains raw population counts by gender and age;
however, the counts for different genders and ages are in different
columns. To compare them more easily, stack the columns end to
end and create factors for gender and age. Start with the stacking
operation.
Stacking The bd.stack function provides the needed stacking operation. Stack
all the population counts for males and females for all ages with one
call to bd.stack:
> censusStack <- bd.stack(census,
columns = 5:40,
replicate = c(1:4, 41:43),
stack.column.name = "pop",
group.column.name = "sexAge")
Table 2.3 lists the arguments to bd.stack.

Table 2.3: Arguments to bd.stack.
Argument Name Description
data Input data set, a bdFrame or data.frame.
columns Names or numbers of columns to be stacked.
replicate Names or numbers of columns to be replicated.
stack.column.name Name of new stacked column.
group.column.name Name of an additional group column to be

created in the output data set. In each output
row, the group column contains the name of the
original column that contained the data value in
the new stacked column.
The first few rows of the resulting data are listed below. Notice the
values for the sexAge variable are the names of the columns that were
stacked.
37
> censusStack
** bdFrame: 1150236 rows, 9 columns **
zipcode lat long popTotal housingTotal own rent
1 601 18180103 -66749472 19143 5895 4232 1663
2 602 18363285 -67180247 42042 13520 10903 2617
3 603 18448619 -67134224 55592 19182 12631 6551
4 604 18498987 -67136995 3844 1089 719 370
5 606 18182151 -66958807 6449 2013 1463 550
pop sexAge
1 712 male.0
2 1648 male.0
3 2049 male.0
4 129 male.0
5 259 male.0
... 1150231 more rows ...
Notice that the census data started with a little over 33,000 rows.
Now, after stacking, there are over 1.15 million rows.
Variable Now create the sex and age factors. There are several ways to do this,
Creation but the most computationally efficient way for large data is to use the
bd.create.columns function, along with the row-oriented expression
language. Before starting, notice that the column names for the
stacked columns (male.0, male.5, ..., female.80, female.85) can be
separated into male and female groups simply by the number of
characters in their names. All male names have seven or fewer
characters and all female names have eight or more characters.
Therefore, by checking the number of characters in the string, you
can determine whether the value should be “male” or “female”. Here
is an example of the row-oriented Expression Language:
" ifelse(nchar(sexAge) > 7, 'female', 'male' "
Notice the use of a single quote, ‘, to embed a quote within a quote.

To create the age variable is a little harder. You must subset the string
differently, depending on whether the value of sexAge corresponds to
a male or female.
1. For males, extract from the sixth character to the end, and for
females, extract from the eighth character to the end. The
row-oriented expression language follows:
38
Data Manipulation
" ifelse(nchar(sexAge) > 7,

substring(sexAge, 8, nchar(sexAge)),
substring(sexAge, 6, nchar(sexAge))) "
2. Create an additional variable that is a measure of the

population size for each age and gender group relative to the
population size for the entire zip code area. Because each row
contains gender and age specific population estimates and the
total population estimate for that zip code area, the relative
population size for each gender and age group is simply
"pop/popTotal"
3. Create all three new variables in a single call to

bd.create.columns (which requires only a single pass
through the data) by including all three of the above
expressions in the call.
> censusStack <- bd.create.columns(censusStack,
exprs = c("ifelse(nchar(sexAge) > 7, 'female', 'male')",
"ifelse(nchar(sexAge) > 7,
substring(sexAge, 8, nchar(sexAge)),
substring(sexAge, 6, nchar(sexAge)))" ,
"pop/popTotal"),
names. = c("sex", "age", "popProp"),
types = c("factor", "character", "numeric"))
In this example, bd.create.columns arguments include the

following:
• exprs takes a character vector of strings; each string is the
expression that creates a different column.
• names supplies the names for the newly-created columns.
• types specifies the type of data in the resulting column.
For more information on bd.create.columns, see its help file
by typing help(bd.create.columns), or by typing
?bd.create.columns in S-PLUS.
Note
The age column in the call to bd.create.columns is stored as a character column so we have
more control when creating an age factor. A discussion of this is included in the next section
Factors.
39
Factors In the previous section, we created age as a character vector, because

when bd.create.columns creates factors, it establishes levels as the
set of alphabetically sorted unique values in the column. The levels are
not arranged numerically. In the example output below, notice the
placement of the “5” between “45” and “50”.
> levels(factor(censusStack[, “age”]))
[1] "0" "10" "15" "20" "25" "30" "35" "40" "45" "5" "50"
[12] "55" "60" "65" "70" "75" "80" "85"
When S-PLUS creates tables or graphics that use the levels as labels,
the order is as the levels are listed, rather than in numerical order.
To control the order of the levels of a factor, call the bdFactor
function directly and state explicitly the order for the levels. For
example, using the census data:
> censusStack[, "age"] <- bdFactor(censusStack[, "age"],
levels = c("0", "5", "10", "15", "20", "25",
"30", "35", "40", "45", "50", "55",
"60", "65", "70", "75", "80", "85"))
40
More Graphics
MORE GRAPHICS
The data is now prepared to allow more interesting graphics. For
example, create an age distribution plot conditional on gender (Figure
2.8) with the following call to bwplot, a Trellis graphic function:
> bwplot(age ~ log(popProp + 0.00001) | sex,
data = censusStack)
Note
0.00001 is added to the population proportions to avoid taking the log of zero.
-10 -8 -6 -4 -2 0
female male
85
80
75
70
65
60
55
50
age
45
40
35
30
25
20
15
10
5
0
-10 -8 -6 -4 -2 0
log(popProp + 1e-005)
Figure 2.8: Boxplots of logged relative population numbers by age and sex.
The following call to bwplot creates a plot (Figure 2.9) of logged

relative population numbers by age and whether the zip code area
contains more than the median number of rental units:
> bwplot(age ~ log(popProp + 0.00001) | rent > 193,
data = censusStack)
41
Note the span of the boxes for 80 and older when there are fewer
than the median number of rental units, implying that the population
numbers for this group drops dramatically in some areas where there
few rental units.
-10 -8 -6 -4 -2 0
FALSE TRUE
85
80
75
70
65
60
55
50
age
45
40
35
30
25
20
15
10
5
0
-10 -8 -6 -4 -2 0
log(popProp + 1e-005)
Figure 2.9: Boxplots of logged relative population numbers by age and rent>193.
Another interesting plot is of the zip code area centers in units of

latitude and longitude. Highly populated areas show a higher density
of zip code numbers; therefore, they show greater density in the
hexbin scatterplot. First, however, notice that the scale of lat and
long is off by a factor of 1,000,000. The lat variable should be in the
range of 20 to 70 and long should be in the range of -60 to -180. So
first rescale these variables by a call to bd.create.columns.
> summary(census[, c("lat", "long")])
lat long
Min.:17964529 Min.:-176636755
Mean:38851462 Mean: -91044543
Max.:71299525 Max.: -65292575
Even more efficient, requiring no passes through the data:
42
More Graphics
> summary(census)[, c("lat", "long")]
Because the summary is stored in metadata, it does not have to be

computed. The first form creates a two-column big data object, and
then gets the summary from that object.
To rescale lat and long simultaneously, use the following
expressions:
"lat/1e6", "long/1e6"
Use the original data set census, rather than censusStack, because
census has just one row per zip code.
> census <- bd.create.columns(census,
exprs=c("lat/1.e6", "long/1.e6"),
names=c("lat","long"))
The values of lat and long are now scaled appropriately:

> summary(census[, c("lat", "long")])
lat long
Min.:17.96453 Min.:-176.63675
Mean:38.85146 Mean: -91.04454
Max.:71.29953 Max.: -65.29257
Or, more efficiently:
> summary(census)[, c("lat", "long")]
Now produce the plot with a simple call to xyplot.
43
> xyplot(lat ~ long, data = census)
70
1200
60
1000
lat 50 800
40 600
400
30
200
20
-180 -160 -140 -120 -100 -80 -60

long
Figure 2.10: Hexbin scatterplot of latitudes and longitudes. Zip codes are denser
where populations are denser, so this plot displays relative population densities.
44
Clustering
CLUSTERING
This section applies clustering techniques to the census data to find
sub populations (collections of zip code areas) with similar age
distributions. The section Modeling Group Membership develops
models that characterize the subgroups we find by clustering.
Data The section Tabular Summaries computed the average age distribution
Preparation across all zip code areas by age and gender, depicted in Figure 2.7.
Next, group zip-code areas by age distribution characteristics, paying
close attention to those that deviate from the national average. For
example, age distributions in areas with military bases, typically
dominated by young adult single males without children, should
stand out from the national average.
Unusual populations are most noticeable if the population
proportions (previously computed as pop/popTotal by age and
gender) are normalized by the national average. One way to
normalize is to divide population proportions in each age and gender
group by the national average for each age and gender group. The
(odds) ratio represents how similar (or dissimilar) a zip-code
population is from the national average. For example, a ratio of 2 for
females 85 years or older indicates that the proportion of women 85
and older is twice that of the national average.
To prepare the population proportions, recall that the national
averages are produced with the colMeans function:
> ageDist <-
colMeans(census[, 5:40] / census[, "popTotal"])
Also recall that, in S-PLUS, if you multiply (or divide) a matrix by a

vector, the elements of each column are multiplied by the
corresponding element of the vector (assuming the length of the
vector is equivalent to the number of rows of the matrix). We want to
divide each element of a column by the mean of that column. In-
memory computation might proceed as follows:
> popPropN <- t(t(census[, 5:40]) / ageDist)
That is, transpose the data matrix, divide by a vector as long as each
column of the transposed matrix, and then transpose the matrix back.
45
The above operation is inefficient for large data. It requires multiple

passes through the data. A more efficient way to compute the
normalized population proportions is to create a series of row-
oriented expressions:
"male.0/ageDist[1]"
and process them with bd.create.columns.

Here is how to do this:
1. Create the proportions matrix:
> popProp <- census[, 5:40] / census[, "popTotal"]
2. Create the expression vector:

> norm.exprs <- paste(names(popProp),
paste("/ageDist[", 1:36, "]",sep=""), sep="")
3. Normalize the population proportions:

> popPropN <- bd.create.columns(popProp,
exprs = norm.exprs,
names. = names(popProp),
row.language = F)
4. Join the normalized population proportions with the rest of

the census data:
censusN <- bd.join(list(census[, c(1:4, 41:43)],
popPropN))
Notes
• In step 3, row.language = F is specified because the expressions use S-PLUS syntax to do

subscripting.
• In step 4, there are no key variables specified in the join operation, which results in a
join by row number.
K-Means You are now ready to do the clustering. The big data version of k-
Clustering means clustering is bdCluster. The important arguments are:
• The data (a bdFrame in this example).
• The columns to cluster (if all columns of the bdFrame are not
included in the clustering operation).
46
Clustering
• The number of clusters, k.

Typically, determining a reasonable value for k requires some effort.
Usually, this involves clustering repeatedly for a sequence of k values
and choosing the k that greatly reduces the residual variance without
adding an excessive number of clusters. For this example, after a little
experimentation, we set k = 40.
> clusterCensusN <- bdCluster(censusN,

columns=names(popPropN),k=40)
Notes
To match the results presented here, set the random seed to 22 before calling bdCluster. To set
the seed, at the prompt, type set.seed(22).
This example focuses on only the age x gender distributions, so columns is set to just those
columns with population counts.
The bdCluster function has a predict method, so you can extract

group membership identifiers for each observation and append them
onto the normalized data, as follows:
> censusNPred <- cbind(censusN, predict(clusterCensusN))
Analyzing the In this section, examine the results of applying k-means clustering to
Results the census data. To get a sense of how big the clusters are and what
they look like, start by combining cluster means and counts.
1. To compute cluster means, call bd.aggregate as follows:
> clusterMeans <- bd.aggregate(censusNPred,
columns = names(popProp),
by.columns="PREDICT.membership",
methods="mean")
2. To compute cluster group sizes, call bd.aggregate again with

“count” as the method:
> clusterCounts <- bd.aggregate(censusNPred,
columns=1,
by.columns="PREDICT.membership",
methods="count")
3. Merge the two aggregates:
47
> clusterMeansCounts <- merge(clusterCounts, clusterMeans)
The call to merge without a key.variables argument matches

on the common columns names, by default.
The clusterMeansCounts object contains mean population estimates
for each zip code area, age and gender. The first 24 groups (ordered
by the number of zip code regions that comprise them) are plotted in
Figure 2.11. The upper left panel corresponds to the group with the
most zip codes and the lower right panel has the fewest. The graphs
that appear top-heavy reflect more older people. Notice the panel in
the third row down, first position on the left. It is very heavily
weighted on the top. These are retirement communities. Also, notice
the second panel from the left in the bottom row. The population is
dominated by young adult males. These are primarily military bases.
k=2 k=4 k=3 k=6 k=5 k=7

N = 5533 N = 4807 N = 4235 N = 3204 N = 2839 N = 1711
k = 10 k=9 k=8 k = 11 k = 14 k = 12
N = 1569 N = 1394 N = 1277 N = 1260 N = 1107 N = 510
k = 13 k = 17 k = 16 k = 15 k = 21 k = 23
N = 480 N = 414 N = 331 N = 321 N = 183 N = 121
k = 22 k = 18 k = 19 k = 20 k = 26 k = 25
N = 110 N = 67 N = 64 N = 60 N = 59 N = 57
Figure 2.11: Age distribution barplots for the first 24 groups resulting from k-means
clustering with 40 groups specified. The horizontal lines in each panel correspond to
20 (the lower one) and 70 years of age. Females are to the left of the vertical and
males are to the right.
To produce Figure 2.11, run the following:
48
Clustering
> source(paste(getenv("SHOME"),
"/samples/bigdata/census/my.vbar.q", sep=""))
> index16 <- rep(1:16, length = 24)
> par(mfrow=c(4,6))
> for(k in 1:24) {
my.vbar(bd.coerce(clusterMeansCounts), k=k,
plotcols=3:38,
Nreport.col=2,
col=1+index16[k])
An interesting graphic that dramatizes group membership displays

each zip code as a single black point for the center of the zip code
region, and then overlays points for any given cluster group in
another color. Technically, this plot is more interesting, because it
uses a new function, bd.block.apply, to process the data a block at a
time.
The bd.block.apply function takes two primary arguments:
• The data, usually a bdFrame, census in this case.
• a function for processing the data a block at a time.
Note
The bd.block.apply argument FUN is an S-PLUS function called to process a data frame. This
function itself cannot perform big data operations, or an error is generated. (This is true for
bd.by.group and bd.by.window, as well.)
Define the block processing function as follows:

f <- function(SP){
par(plt = c(.1, 1, .1, 1))
if(SP$in1.pos == 1){
plot(SP$in1[,"long"], SP$in1[, "lat"],
pch = 1, cex = 0.15,
xlim=c(-125,-70), ylim=c(25, 50),
xlab="", ylab="", axes = F)
axis(1, cex = 0.5)
axis(2, cex = 0.5)
title(xlab = "Longitude", ylab = "Latitude")
} else {
49
points(SP$in1[, "long"], SP$in1[, "lat"], cex =

0.2)
}
}
This function processes a list object, which contains one block of the
census bdFrame. SP$in1 corresponds to the data, and SP$in1.pos
corresponds to the starting row position of each block of the bdFrame
that is passed to the function. The test if(SP$in1.pos == 1) checks if
the first block is being processed. If the first block is processed, a call
to plot is made; if the first block is not processed, a call to points is
made. The call to bd.block.apply is:
> bd.block.apply(census, FUN = f)
This call makes this new graph select only those rows that belong to
the cluster group of interest, and then coerce it to a data frame to
demonstrate the simplicity of using both bdFrame and a data.frame
objects in the same function. Start by keeping only those variables
that are useful for displaying the cluster group locations.
> censusNPsub <- bd.filter.columns(censusNPred,
keep = c("lat","long","PREDICT.membership"))
50
Clustering
Figure 2.12: Plot of all zip code region centers with cluster group 20 overlaid in
another color. The double histogram in the bottom left corner displays the age
distributions for females to the left and males to the right for cluster group 20. The
horizontal lines in the histogram are at 20 and 70 years of age.
To generate graphs for the first 22 cluster groups, it is slightly more

work:
> pred <- clusterMeansCounts[, "PREDICT.membership"]
> for(k in 1:22) {
> setk <- bd.coerce(bd.filter.rows(censusNPsub,
expr = "PREDICT.membership == pred[k]",
columns = c("lat", "long"),
row.language = F))
par(plt=c(.1, 1, .1, 1))
bd.block.apply(census, FUN = f)
points(setk[, "long"], setk[, "lat"],
col=1+index16[k],
cex=0.6, pch=16)
par(new=T)
51
par(plt=c(.1, .3, .1, .3))

my.vbar(clusterMeansCounts, k=k, plotcols=3:38,
Nreport.col=2, col=1+index16[k])
box()
}
Notes
1. setkis created as a regular data frame using bd.coerce, assuming that once a
given cluster group is selected the data is small enough to process it entirely in
memory.
2. bd.block.apply is used to plot all the zip code region centers, which requires
processing the entire bdFrame.
3. setk contains the latitude and longitude locations for zip code centers for the
selected group, pred[k]
4. setk was created to demonstrate the use of both bdFrame objects and data.frame
objects in a single function. Placing the cluster group points on the graph could
also be accomplished in the function passed to bd.block.apply.
52
Modeling Group Membership
MODELING GROUP MEMBERSHIP

The age distributions in Figure 2.11 are intriguing, but we know little
about why the ages are distributed the way they are. Except for
obvious deductions like retirement communities and military bases,
we do not have much more information in the current data set.
Another data set, censusDemogr, provides additional demographics
variables such as household income, education and marital status.
By modeling group membership as a function of an assortment of
explanatory variables, we can characterize the groups relative to
those variables. The data in censusDemogr contains the variables
listed in Table 2.4. Note that all the variables except housingTotal
and the cluster group variables at the end contain the proportion of
households (hh) with the characteristic stated in the description
column.
Table 2.4: Variables contained in censusDemogr, a bdFrame object. All variables,
except housingTotal, contain the proportion of households (hh) in the zip code area
with the stated characteristic.
Variable Description
housingTotal Total number of housing units.
own Own residence.
onePlusPersonHouse Two or more family members in hh.
nonFamily Two or more non-family members in hh.
Plus65InHouse 65 or older in family hh.
Plus65InNonFamily 65 or older in non-family hh.
Plus65InGroup 65 or older in group quarters.
marriedChildren Married-couple families with children.
marriedNoChildren Married-couple families without children.
53

maleChildren Male householder with children.
maleNoChildren Male householder without children.
femaleChildren Female householder with children.
femaleNoChildren Female householder without children.
maleSingle Single male.
femaleSingle Single female.
maleMarried Married male.
femaleMarried Married female.
maleWidow Male widower.
femaleWidow Female widow.
maleDiv Male divorced.
femaleDiv Female divorced.
english5to17 5 - 17 year olds speak only English.
english18to65 18 - 65 year olds speak only English.
englishOver65 Over 65 year olds speak only English.
native Born in US.
entryToUS95to00 Entry to US from 1995 to 2000.
54

entryToUSBefore65 Entry to US before 1965.
changedHouseSince95 Changed residence since 1995.
maleLoEd Male head of household with low education.
femaleLoEd Female head of hh with low education.
maleHS Male head of hh with HS education.
femaleHS Female head of hh with HS education.
maleCollege Male head of hh with college education.
femaleCollege Female head of hh with college education.
maleBA Male head of hh with bachelor’s degree.
femaleBA Female head of hh with bachelor’s degree.
maleAdvDeg Male head of hh with advanced degree.
55

femaleAdvDeg Female head of hh with advanced degree.
maleWorked99 Male head of hh worked in 1999.
femaleWorked99 Female head of hh worked in 1999.
maleBlueCollar Male head of hh blue-collar worker.
femaleBlueCollar Female head of hh blue-collar worker.
maleWhiteCollar Male head of hh white-collar worker.
femaleWhiteCollar Female head of hh white-collar worker.
houseUnder30K hh income under $30K.
house30to60K hh income $30K - $60K.
house60to200K hh income $60K - $200K.
houseOver200K hh income over $200K.
houseWithSalary hh with salary income.
houseSelfEmpl hh with self-employment income.
houseInterestEtc hh with interest and other investment income.
houseSS hh with social security income.
housePubAssist hh with public assistance income.
houseRetired Head of hh retired.
56

houseNotVacant House not vacant.
houseOwnerOccupied House owner occupied.
group18 Cluster group18.
Building a The cluster group membership variables are binary with “yes” or
Model “no”, indicating group membership for each zip code area. To get a
sense of group membership characteristics, you can create a logistic
model for each group of interest using glm, which has been extended
to handle bdFrame objects. The syntax is identical to that of glm with
regular data frames.The model specification is as follows:
> group18Fit <- glm(group18 ~ ., data = censusDemogr,

family = binomial)
And the output is similar:
> group18Fit
Call:
bdGlm(formula = group18 ~ ., family = binomial, data
= censusDemogr)
Coefficients:
(Intercept) housingTotal own
-51.49204 0.0002713171 -0.0005471851
onePlusPersonHouse nonFamily Plus65InHouse

3.560468 10.21905 18.44271
.
.
.
Degrees of freedom: 31951 total; 31888 residual
57
Residual Deviance: 5445.941
Note
The glm function call is the same as for regular in-memory data frames; however, the extended
version of glm in the bigdata library applies appropriate methods to bdFrame data by initiating a
call to bdGlm. The call expression shows the actual call went to bdGlm.
Summarizing You can apply the usual operations (for example, summary, coef,
the Fit plot) to the resulting fit object. The plots are displayed as hexbin
scatterplots because of the volume of data.
> plot(group18Fit)
4
Counts
31780
30000
28000
2
26000
24000
Residuals
22000
20000
18000
16000
0
14000
12000
10000
8000
6000
4000
-2
2000
1
0.0 0.2 0.4 0.6 0.8 1.0

Fitted : housingTotal + own + onePlusPersonHouse + nonFamily + Plus65InHouse + P .
Figure 2.13: Residuals vs. fitted values resulting from modeling cluster group 18
membership as a function of census demographics.
Characterizing To characterize the group, examine the significant coefficients as

the Group follows:
> group18Coeff <- summary(group18Fit)[["coef"]]
58
> group18Coeff[abs(group18Coeff[,"t value"])

> qnorm(0.975),]
Value Std. Error t value
(Intercept) -51.492043 13.866083 -3.713525
nonFamily 10.219051 4.079199 2.505161
Plus65InHouse 18.442709 6.172655 2.987808
Plus65InNonFamily 19.186751 5.953835 3.222587
maleSingle 39.541568 9.123876 4.333857
femaleWidow 23.710092 10.332282 2.294759
maleDiv 23.374178 8.807237 2.653974
changedHouseSince95 6.253725 2.492780 2.508735
femaleLoEd -12.132175 2.986016 -4.062997
maleCollege 5.820187 2.897105 2.008966
femaleBA -9.518559 3.518594 -2.705217
maleAdvDeg 10.536835 3.553861 2.964898
femaleAdvDeg -7.932499 3.568260 -2.223072
maleWorked99 6.598822 2.787717 2.367107
femaleWorked99 7.200051 3.244321 2.219278
To interpret the above table, note that positive coefficients predict

group 18 membership and negative coefficients predict non-group
membership. With that understanding, group 18 members are more
likely:
• In non-family households that have changed location in the
last 5 years.
• Single or divorced males or widowed females.
• Males with some college education and frequently with
advanced degrees who worked the previous year.
Cluster group 18 corresponds to zip code regions dominated by
young adult males, typical of military bases and penal institutions.
59
60
CREATING GRAPHICAL
DISPLAYS OF LARGE DATA
SETS
3
Introduction 62
Overview of Graph Functions 63
Functions Supporting Graphs 63
Example Graphs 69
Plotting Using Hexagonal Binning 69
Adding Reference Lines 74
Plotting by Summarizing Data 79
Creating Graphs with Preprocessing Functions 90
Unsupported Functions 103
61
Chapter 3 Creating Graphical Displays of Large Data Sets
INTRODUCTION
This chapter includes information on the following:
• An overview of the graph functions available in the Big Data
Library, listed according to whether they take a big data
object directly, or require a preprocessing function to produce
a chart.
• Procedures for creating plots, traditional graphs, and Trellis
graphs.
Note
In Microsoft Windows, editable graphs in the graphical user interface (GUI) do not support big
data objects. To use these graphs, create an S-Plus data.frame containing either all of the data or
a sample of the data.
62
Overview of Graph Functions
OVERVIEW OF GRAPH FUNCTIONS

The Big Data Library supports most (but not all) of the traditional and
Trellis graph functions available in the S-PLUS library. The design of
graph support for big data can be attributed to practical application.
For example, if you had a data set of a million rows or tens of
thousands of columns, a cloud chart would produce an illegible plot.
Functions This section lists the functions that produce graphs for big data
Supporting objects. If you are unfamiliar with plotting and graph functions in
S-PLUS, review the Guide to Graphics.
Graphs
Implementing plotting and graph functions to support large data sets
requires an intelligent way to handle thousands of data points. To
address this need, the graph functions to support big data are
designed in the following categories:
• Functions to plot big data objects without preprocessing,
including:
• Functions to plot big data objects by hexagonal binning.
• Functions to plot big data objects by summarizing data in
a plot-specific manner.
• Functions providing the preprocessing support for plotting big
data objects.
• Functions requiring preprocessing support to plot big data
objects.
The following sections list the functions, organized into these
categories. For an alphabetical list of graph functions supporting big
data objects, see the Appendix.
Using cloud or parallel results in an error message. Instead, sample
or aggregate the data to create a data.frame that can be plotted using
these functions.
63
Graph Functions The following functions can plot a large data set (that is, can accept a
using Hexagonal big data object without preprocessing) by plotting large amounts of
Binning data using hexagonal binning.
Table 3.1: Functions for plotting big data using hexagonal binning.
Function Comment
pairs Can accept a bdFrame object.
plot Can accept a hexbin, a single bdVector, two bdVectors,

or a bdFrame object.
splom Creates a Trellis graphic object of a scatterplot matrix.
xyplot Creates a Trellis graphic object, which graphs one set

of numerical values on a vertical scale against another
set of numerical values on a horizontal scale.
Functions Adding Reference Lines to Plots

The following functions add reference lines to hexbin plots.
Table 3.2: Functions that add reference lines to hexbin plots.
Function Type of line
abline(lsfit()) Regression line.
lines(loess.smooth()) Loess smoother.
lines(smooth.spline()) Smoothing spline.
panel.lmline Adds a least squares line to an

xyplot in a Trellis graph.
64
Table 3.2: Functions that add reference lines to hexbin plots. (Continued)
Function Type of line
panel.loess Adds a loess smoother to an xyplot

in a Trellis graph.
qqline() QQ-plot reference line.
xyplot(lmline=T) Adds a least squares line to an

xyplot in a Trellis graph.
Graph Functions The following functions summarize data in a plot-specific manner to

Summarizing plot big data objects.
Data Table 3.3: Functions that summarize in plot-specific manner.
Function Description
boxplot Produces side by side boxplots from a number of

vectors. The boxplots can be made to display the
variability of the median, and can have variable widths
to represent differences in sample size.
bwplot Produces a box and whisker Trellis graph, which you

can use to compare the distributions of several data
sets.
plot(density) density returns x and y coordinates of a non-

parametric estimate of the probability density of the
data.
densityplot Produces a Trellis graph demonstrating the

distribution of a single set of data.
hist Creates a histogram.
histogram Creates a histogram in a Trellis graph.
qq Creates a Trellis graphic object comparing the

distributions of two sets of data
65
Table 3.3: Functions that summarize in plot-specific manner. (Continued)
qqmath Creates normal probability plot for only one data

object in a Trellis graph. qqmath can also make
probability plots for other distributions. It has an
argument distribution whose input is any function that
computes quantiles.
qqnorm Creates normal probability plot in a Trellis graph.

qqnorm can accept a single bdVector object.
qqplot Creates normal probability plot in a Trellis graph. Can

accept two bdVector objects. In qqplot, each vector or
bdVector is taken as a sample, for the x- and y-axis
values of an empirical probability plot.
stripplot Creates a Trellis graphic object similar to a box plot in

layout; however, it displays the density of the
datapoints as shaded boxes.
Functions The following functions are used to preprocess large data sets for
Providing graphing:
Support to Table 3.4: Functions used for preprocessing large data sets.
Preprocess Data
for Graphing Function Description
aggregate Splits up data by time period or other factors

and computes summary for each subset.
hexbin Creates an object of class hexbin. Its basic

components are a cell identifier and a count of
the points falling into each occupied cell.
hist2d Returns a structure for a 2-dimensional

histogram which can be given to a graphics
function such as image or persp.
interp Interpolates the value of the third variable onto

an evenly spaced grid of the first two variables.
66
Table 3.4: Functions used for preprocessing large data sets. (Continued)
loess Fits a local regression model.
loess.smooth Returns a list of values at which the loess curve

is evaluated.
lsfit Fits a (weighted) least squares multivariate

regression.
smooth.spline Fits a cubic B-spline smooth to the input data.
table Returns a contingency table (array) with the

same number of dimensions as arguments
given.
tapply Partitions a vector according to one or more

categorical indices.
Functions The following functions do not accept a big data object directly to
Requiring create a graph; rather, they require one of the specified preprocessing
Preprocessing functions.
Support for Table 3.5: Functions requiring preprocessors for graphing
Graphing large data sets.
Function Preprocessors Description
barchart table, tapply, Creates a bar chart in a Trellis

aggregate graph.
barplot table, tapply, Creates a bar graph.

aggregate
contour interp, hist2d Make a contour plot and possibly

return coordinates of contour lines.
contourplot loess Displays contour plots and level

plots in a Trellis graph.
67
Table 3.5: Functions requiring preprocessors for graphing

large data sets. (Continued)
Function Preprocessors Description
dotchart table, tapply, Plots a dot chart from a vector.

aggregate
dotplot table, tapply, Creates a Trellis graph, displaying

aggregate dots and labels.
image interp, hist2d Creates an image, under some

graphics devices, of shades of gray
or colors that represent a third
dimension.
levelplot loess Displays a level plot in a Trellis

graph.
persp interp, hist2d Creates a perspective plot, given a

matrix that represents heights on an
evenly spaced grid.
pie table, tapply, Creates a pie chart from a vector of

aggregate data.
piechart table, tapply, Creates a pie chart in a Trellis graph

aggregate
wireframe loess Displays a three-dimensional

wireframe plot in a Trellis graph.
68
Example Graphs
EXAMPLE GRAPHS
The examples in this chapter require that you have the Big Data
Library loaded. The examples are not large data sets; rather, they are
small data objects that you convert to big data objects to demonstrate
using the Big Data Library graphing functions.
Plotting Using Hexagonal binning plots are available for:

Hexagonal • Single plot (plot)
Binning • Matrix of plots (pairs)
• Conditioned single or matrix plots (xyplot)
Functions that evaluate data over a grid in standard S-PLUS aggregate
the data over the grid (such as binning the data and taking the mean
in each grid cell, and then plot the aggregated values) when applied to
a big data object.
Hexagonal binning is a data grouping or reduction method typically
used on large data sets to clarify a spatial display structure in two
dimensions. Think of it as partitioning a scatter plot into larger units
to reduce dimensionality, while maintaining a measure of data clarity.
Each unit of data is displayed with a hexagon and represents a bin of
points in the plot. Hexagons are used instead of squares or rectangles
to avoid misleading structure that occurs when edges of the rectangles
line up exactly.
Plotting using hexagonal binning is the standard technique used when
a plotting function that currently plots one point per row is applied to
a big data object.
Plotting using hexagonal bins is available for a single plot, a matrix of
plots, and conditioned single or matrix plots.
69
The Census example introduced in Chapter 2 demonstrates plotting

using hexagonal binning (see Figure 2.6). When you create a plot
showing a distribution of zip codes by latitude and longitude, the
following simple plot is displayed:
Figure 3.1: Example of graph showing hexagonal binning.
The functions listed in Table 3.1 support big data objects by using
hexagonal binning. This section shows examples of how to call these
functions for a big data object.
Create a Pair- The pairs function creates a figure that contains a scatter plot for
wise Scatter Plot each pair of variables in a bdFrame object.
To create a sample pair-wise scatter plot for the fuel.frame bdFrame
object, in the Commands window, type the following:
pairs(as.bdFrame(fuel.frame))
70
Example Graphs
The pair-wise scatter plot appears as follows:

fif
Figure 3.2: Graph using pairs for a bdFrame.
This scatter plot looks similar to the one created by calling

pairs(fuel.frame); however, close examination shows that the plot
is composed of hexagons.
Create a Single The plot function can accept a hexbin object, a single bdVector, two
Plot bdVectors, or a bdFrame object. The following example plots a simple
hexbin plot using the weight and mileage vectors of the fuel.bd
object.
To create a sample single plot, in the Commands window, type the
following:
fuel.bd <- as.bdFrame(fuel.frame)

plot(hexbin(fuel.bd$Weight, fuel.bd$Mileage))
71
The hexbin plot is displayed as follows:
Figure 3.3: Graph using single hexbin plot for fuel.bd.
Create a Multi- The function splom creates a Trellis graph of a scatterplot matrix. The
Panel Scatterplot scatterplot matrix is a good tool for displaying measurements of three
Matrix or more variables.
To create a sample multi-panel scatterplot matrix, where you create a
hexbin plot of the columns in fuel.bd against each other, in the
Commands window, type the following:

splom(~., data=fuel.bd)
Note
Trellis functions in the Big Data Library require the data argument. You cannot use formulas
that refer to bdVectors that are not in a specified bdFrame.
Notice that the ‘.’ is interpreted as all columns in the data set
specified by data.
72
Example Graphs
The splom plot is displayed as follows:
Figure 3.4: Graph using splom for fuel.bd.
To remove a column, use -term. To add a column, use +term. For

example, the following code replaces the column Disp. with its log.

splom(~.-Disp.+log(Disp.), data=fuel.bd)
Figure 3.5: Graph using splom to designate a formula for fuel.bd
For more information about splom, see its help topic.
73
Create a The function xyplot creates a Trellis graph, which graphs one set of
Conditioning Plot numerical values on a vertical scale against another set of numerical
or Scatter Plot values on a horizontal scale.
To create a sample conditioning plot, in the Commands window,
type the following:
xyplot(data=as.bdFrame(air),
ozone~radiation|temperature,
shingle.args=list(n=4), lmline=T)
The variable on the left of the ~ goes on the vertical (or y) axis, and
the variable on the right goes on the horizontal (or x) axis.
The function xyplot contains the default argument lmline=T to add
the approximate least squares line to a panel quickly. This argument
performs the same action as panel.lmline in standard S-PLUS.
The xyplot plot is displayed as follows:
Figure 3.6: Graph using xyplot with lmline=T.
Trellis functions in the Big Data Library handle continuous “given”

variables differently than standard data Trellis functions: they are sent
through equal.count, rather than factor.
Adding You can add a regression line or scatterplot smoother to hexbin plots.
Reference The regression line or smoother is a weighted fit, based on the binned
values.
Lines
74
Example Graphs
The following functions add the following types of reference lines to

hexbin plots:
• A regression line with abline
• A Loess smoother with loess.smooth
• A smooth spline with smooth.spline
• A line to a qqplot with qqline
• A least squares line to an xyplot in a Trellis graph.
For smooth.spline and loess.smooth, when the data consists of
bdVectors, the data is aggregated before smoothing. The range of the
x variable is divided into 1000 bins, and then the mean for x and y is
computed in each bin. A weighted smooth is then computed on the
bin means, weighted based on the bin counts. This computation
results in values that differ somewhat from those where the smoother
is applied to the unaggregated data. The values are usually close
enough to be indistinguishable when used in a plot, but the difference
could be important when the smoother is used for prediction or
optimization.
Add a Regression When you create a scatterplot from your large data set, and you
Line notice a linear association between the y-axis variable and the x-axis
variable, you might want to display a straight line that has been fit to
the data. Call lsfit to perform a least squares regression, and then
use that regression to plot a regression line.
The following example draws an abline on the chart that plots
fuel.bd weight and mileage data. First, create a hexbin object and
plot it, and then add the abline to the plot.
To add a regression line to a sample plot, in the Commands window,
type the following:

hexbin.out <- plot(fuel.bd$Weight, fuel.bd$Mileage)
# displays a hexbin plot
# use add.to.hexbin to keep the abline within the
# hexbin area. If you just call abline, then the
# line might draw outside of the hexbin and interfere
# with the label.
add.to.hexbin(hexbin.out, abline(lsfit(fuel.bd$Weight,
fuel.bd$Mileage)))
75
The resulting chart is displayed as follows:
Figure 3.7: Graph drawing an abline in a hexbin plot.
Add a Loess Use lines(loess.smooth) to add a smooth curved line to a scatter

Smoother plot.
To add a loess smoother to a sample plot, in the Commands
window, type the following:

add.to.hexbin(hexbin.out,
lines(loess.smooth(fuel.bd$Weight,
fuel.bd$Mileage), lty=2))
76
Example Graphs
Figure 3.8: Graph using loess.smooth in a hexbin plot.
Add a Smoothing Use lines(smooth.spline) to add a smoothing spline to a scatter

Spline plot.
To add a smoothing spline to a sample plot, in the Commands

add.to.hexbin(hexbin.out,
lines(smooth.spline(fuel.bd$Weight,
fuel.bd$Mileage),lty=3))
77
Figure 3.9: Graph using smooth.spline in a hexbin plot.
Add a Least To add a reference line to an xyplot, set lmline=T. Alternatively, you
Squares Line to can call panel.lmline or panel.loess. See the section Create a
an xyplot Conditioning Plot or Scatter Plot on page 74 for an example.
Add a qqplot The function qqline fits and plots a line through a normal qqplot.
Reference Line To add a qqline reference line to a sample qqplot, in the

qqnorm(fuel.bd$Mileage)
qqline(fuel.bd$Mileage)
78
Example Graphs
The qqline chart is displayed as follows:
Figure 3.10: Graph using qqline in a qqplot chart.
Plotting by The following examples demonstrate functions that summarize data

Summarizing in a plot-specific manner to plot big data objects. These functions do
not use hexagonal binning. Because the plots for these functions are
Data always monotonically increasing, hexagonal binning would obscure
the results. Rather, summarizing provides the appropriate
information.
Create a Box Plot The following example creates a simple box plot from fuel.bd. To
create a Trellis box and whisker plot, see the following section.
To create a sample box plot, in the Commands window, type the
following:

boxplot(split(fuel.bd$Fuel, fuel.bd$Type), style.bxp="att")
79
The box plot is displayed as follows:
Figure 3.11: Graph using boxplot.
Create a Trellis The box and whisker plot provides graphical representation showing
Box and Whisker the center and spread of a distribution.
Plot To create a sample box and whisker plot in a Trellis graph, in the
bwplot(Type~Fuel, data=(as.bdFrame(fuel.frame)))
The box and whisker plot is displayed as follows:
Figure 3.12: Graph using bwplot.
80
Example Graphs
For more information about bwplot, see Chapter 3, Traditional

Trellis Graphics, in the Guide to Graphics.
Create a Density The density function returns x and y coordinates of a non-parametric

Plot estimate of the probability density of the data. Options include the
choice of the window to use and the number of points at which to
estimate the density. Weights may also be supplied.
Density estimation is essentially a smoothing operation. Inevitably
there is a trade-off between bias in the estimate and the estimate's
variability: wide windows produce smooth estimates that may hide
local features of the density.
Density summarizes data. That is, when the data is a bdVector, the
data is aggregated before smoothing. The range of the x variable is
divided into 1000 bins, and the mean for x is computed in each bin. A
weighted density estimate is then computed on the bin means,
weighted based on the bin counts. This calculation gives values that
differ somewhat from those when density is applied to the
unaggregated data. The values are usually close enough to be
indistinguishable when used in a plot, but the difference could be
important when density is used for prediction or optimization.
To plot density, use the plot function.
To create a sample density plot from fuel.bd, in the Commands

plot(density(fuel.bd$Weight), type="l")
81
The density plot is displayed as follows:
Figure 3.13: Graph using density
Create a Trellis The following example creates a Trellis graph of a density plot, which
Density Plot displays the shape of a distribution. You can use the Trellis density
plot for analyzing a one-dimensional data distribution. A density plot
displays an estimate of the underlying probability density function for
a data set, allowing you to approximate the probability that your data
fall in any interval.
To create a sample Trellis density plot, in the Commands window,
type the following:
singer.bd <- as.bdFrame(singer)

densityplot( ~ height | voice.part, data = singer.bd,
layout = c(2, 4), aspect= 1, xlab = "Height (inches)",
width = 5)
82
Example Graphs
The Trellis density plot is displayed as follows:
Figure 3.14: Graph using densityplot.
For more information about Trellis density plots, see Chapter 3,

Traditional Trellis Graphics, in the Guide to Graphics.
Create a Simple A histogram displays the number of data points that fall in each of a
Histogram specified number of intervals. A histogram gives an indication of the
relative density of the data points along the horizontal axis. For this
reason, density plots are often superposed with (scaled) histograms.
To create a sample hist chart of a full dataset for a numeric vector, in
the Commands window, type the following:

hist(fuel.bd$Weight)
83
The numeric hist chart is displayed as follows:
Figure 3.15: Graph using hist for numeric data.
To create a sample hist chart of a full dataset for a factor column, in


hist(fuel.bd$Type)
The factor hist chart is displayed as follows:
Figure 3.16: Graph using hist for factor data.
84
Example Graphs
Create a Trellis The histogram function for a Trellis graph is histogram.

Histogram To create a sample Trellis histogram, in the Commands window,
type the following:

histogram( ~ height | voice.part, data = singer.bd,
nint = 17, endpoints = c(59.5, 76.5), layout = c(2,4),
aspect = 1, xlab = "Height (inches)")
The Trellis histogram chart is displayed as follows:
Figure 3.17: Graph using histogram.
For more information about Trellis histograms, see Chapter 3,

Traditional Trellis Graphics, in the Guide to Graphics.
Create a The functions qq, qqmath, qqnorm, and qqplot create an ordinary x-y
Quantile-Quantile plot of 500 evenly-spaced quantiles of data.
(QQ) Plot for The function qq creates a Trellis graph comparing the distributions of
Comparing two sets of data. Quantiles of one dataset are graphed against
Multiple corresponding quantiles of the other data set.
Distributions
To create a sample qq plot, in the Commands window, type the
following:

qq((Type=="Compact")~Mileage, data = fuel.bd)
85
The factor on the left side of the ~ must have exactly two levels
(fuel.bd$Compact has five levels).
The qq plot is displayed as follows:
f
Figure 3.18: Graph using qq.
(Note that in this example, by setting Type to the logical Compact, the
labels are set to FALSE and TRUE on the x and y axis, respectively.)
Create a QQ Plot The function qqmath creates normal probability plot in a Trellis
Using a graph. that is, the ordered data are graphed against quantiles of the
Theoretical or standard normal distribution.
Empirical qqmath can also make probability plots for other distributions. It has
Distribution an argument distribution, whose input is any function that
computes quantiles. The default for distribution is qnorm. If you set
distribution = qexp, the result is an exponential probability plot.
To create a sample qqmath plot, in the Commands window, type the

following:

qqmath( ~ height | voice.part, data = singer.bd,
layout = c(2, 4), aspect = 1,
xlab = "Unit Normal Quantile",
ylab = "Height (inches)")
86
Example Graphs
The qqmath plot is displayed as follows:
Figure 3.19: Graph using qqmath.
Create a Single The function qqnorm creates a plot using a single bdVector object. The
Vector QQ Plot following example creates a plot from the mileage vector of the
fuel.bd object.
To create a sample qqnorm plot, in the Commands window, type the

following:

qqnorm(fuel.bd$Mileage)
87
The qqnorm plot is displayed as follows:
Figure 3.20: Graph using qqnorm.
Create a Two The function qqplot creates a hexbin plot using two bdVectors. The
Vector QQ Plot quantile-quantile plot is a good tool for determining a good
approximation to a data set’s distribution. In a qqplot, the ordered
data are graphed against quantiles of a known theoretical distribution.
To create a sample two-vector qqplot, In the Commands window,
type the following:

qqplot(fuel.bd$Mileage, runif(length(fuel.bd$Mileage),
bigdata=T))
Note that in this example, the required y argument for qqplot is

runif(length(fuel.bd$Mileage): the random generation for the
uniform distribution for the vector fuel.bd$Mileage. Also note that
using runif with a big data object requires that you set the runif
argument bigdata=T.
The qqplot plot is displayed as follows:
88
Example Graphs
Figure 3.21: Graph using qqplot.
Create a One- The function stripplot creates a Trellis graph similar to a box plot in
Dimensional layout; however, the individual data points are shown instead of the
Scatter Plot box plot summary.
To create sample one-dimensional scatter plot, in the Commands

stripplot(voice.part ~ jitter(height),
data = singer.bd, aspect = 1,
xlab = "Height (inches)")
89
The stripplot plot is displayed as follows:
Figure 3.22: Graph using stripplot for singer.bd.
Creating The functions discussed in this section do not accept a big data object
Graphs with directly to create a graph; rather, they require a preprocessing
function such as those listed in the section Functions Providing
Preprocessing Support to Preprocess Data for Graphing on page 66.
Functions
Create a Bar Calling barchart directly on a large data set produces a large number
Chart of bars, which results in an illegible plot.
• If your data contains a small number of cases, convert the
data to a standard data.frame before calling barchart.
• If your data contains a large number of cases, first use
aggregate, and then use bd.coerce to create the appropriate
small data set.
In the following example, sum the yields over sites to get the total
yearly yield for each variety.
90
Example Graphs
To create a sample bar chart, in the Commands window, type the

following:
barley.bd <- as.bdFrame(barley)

temp.df <- bd.coerce(aggregate(barley.bd$yield,
list(year=barley.bd$year,
variety=barley.bd$variety), sum))
barchart(variety ~ x | year, data = temp.df,
aspect = 0.4,xlab = "Barley Yield (bushels/acre)")
The resulting bar chart appears as follows:
Figure 3.23: Graph using barchart .
Create a Bar Plot The following example creates a simple bar plot from fuel.bd, using
table to preprocess data.
To create a sample bar plot using table to preprocess the data, in the

barplot(table(fuel.bd$Type), names=levels(fuel.bd$Type),
ylab="Count")
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The bar plot is displayed as follows:
Figure 3.24: Graph using barplot.
To create a sample bar plot using tapply to preprocess the data, in


barplot(tapply(fuel.bd$Mileage, fuel.bd$Type, mean),
names=levels(fuel.bd$Type), ylab="Average Mileage")
The bar plot is displayed as follows:
Figure 3.25: Graph using tapply to create a bar plot.
92
Example Graphs
Create a Contour A contour plot is a representation of three-dimensional data in a flat,

Plot two-dimensional plane. Each contour line represents a height in the z
direction from the corresponding three-dimensional surface. A level
plot is essentially identical to a contour plot, but it has default options
that allow you to view a particular surface differently.
The following example creates a contour plot from fuel.bd, using
interp to preprocess data. For more information about interp, see
the section Visualizing Three-Dimensional Data in the Application
Developer’s Guide.
Like density, interp and loess summarize the data. That is, when
the data is a bdVector, the data is aggregated before smoothing. The
range of the x variable is divided into 1000 bins, and the mean for x
computed in each bin. See the section Create a Density Plot on page
81 for more information.
To create a sample contour plot using interp to preprocess the data,
in the Commands window, type the following:

contour(interp(fuel.bd$Weight, fuel.bd$Disp.,
fuel.bd$Mileage))
The contour plot is displayed as follows:
Figure 3.26: Graph using interp to create a contour plot.
Create a Trellis The function contourplot creates a Trellis contour plot. The
Contour Plot contourplot function creates a Trellis graph of a contour plot. For big
data sets, contourplot requires a preprocessing function such as
loess.
93
The following example creates a contour plot of predictions from

loess.
To create a sample Trellis contour plot using loess to preprocess

data, in the Commands window, type the following:
environ.bd <- as.bdFrame(environmental)

{
ozo.m <- loess((ozone^(1/3)) ~
wind * temperature * radiation,data = environ.bd,
parametric = c("radiation", "wind"),
span = 1, degree = 2)
w.marginal <- seq(min(environ.bd$wind),
max(environ.bd$wind), length = 50)
t.marginal <- seq(min(environ.bd$temperature),
max(environ.bd$temperature), length = 50)
r.marginal <- seq(min(environ.bd$radiation),
max(environ.bd$radiation), length = 4)
wtr.marginal <- list(wind = w.marginal,
temperature = t.marginal, radiation = r.marginal)
grid <- expand.grid(wtr.marginal)
grid[, "fit"] <- c(predict(ozo.m, grid))
print(contourplot(fit ~ wind * temperature | radiation,
data = grid, xlab = "Wind Speed (mph)",
ylab = "Temperature (F)",
main = "Cube Root Ozone (cube root ppb)"))
}
94
Example Graphs
The Trellis contour plot is displayed as follows:
Figure 3.27: Graph using loess to create a Trellis contour plot.
Create a Dot When you create a dot chart, you can use a grouping variable and
Chart group summary, along with other options. The function dotchart can
be preprocessed using either table or tapply.
To create a sample dot chart using table to preprocess data, in the

dotchart(table(fuel.bd$Type), labels=levels(fuel.bd$Type),
xlab="Count")
95
The dot chart is displayed as follows:
Figure 3.28: Graph using table to create a dot chart.
To create a sample dot chart using tapply to preprocess data, in the


dotchart(tapply(fuel.bd$Mileage, fuel.bd$Type, median),
labels=levels(fuel.bd$Type), xlab="Median Mileage")
The dot chart is displayed as follows:
Figure 3.29: Graph using tapply to create a dot chart.
96
Example Graphs
Create a Dot Plot The function dotplot creates a Trellis graph that displays that
displays dots and gridlines to mark the data values in dot plots. The
dot plot reduces most data comparisons to straightforward length
comparisons on a common scale.
When using dotplot on a big data object, call dotplot after using
aggregate to reduce size of data.
In the following example, sum the barley yields over sites to get the
total yearly yield for each variety.
To create a sample dot plot, in the Commands window, type the
following:

list(year=barley.bd$year, variety=barley.bd$variety),
sum))
(dotplot(variety ~ x | year, data = temp.df,
aspect = 0.4, xlab = "Barley Yield (bushels/acre)"))
The resulting Trellis dot plot appears as follows:
Figure 3.30: Graph using aggregate to create a dot chart.
Create an Image The following example creates an image graph using hist2d to
Graph Using preprocess data. The function image creates an image, under some
hist2d graphics devices, of shades of gray or colors that represent a third
dimension.
97
To create a sample image plot using hist2d preprocess the data, in


image(hist2d(fuel.bd$Weight, fuel.bd$Mileage, nx=9, ny=9))
The image plot is displayed as follows:
Figure 3.31: Graph using hist2d to create an image plot.
Create a Trellis The levelplot function creates a Trellis graph of a level plot. For big
Level Plot data sets, levelplot requires a preprocessing function such as loess.
A level plot is essentially identical to a contour plot, but it has default
options so you can view a particular surface differently. Like contour
plots, level plots are representations of three-dimensional data in flat,
two-dimensional planes. Instead of using contour lines to indicate
heights in the z direction, level plots use colors. The following
example produces a level plot of predictions from loess.
To create a sample Trellis level plot using loess to preprocess the

{
wind * temperature * radiation, data = environ.bd,
98
Example Graphs

print(levelplot(fit ~ wind * temperature | radiation,
}
The level plot is displayed as follows:
Figure 3.32: Graph using loess to create a level plot.
Create a persp The persp function creates a perspective plot given a matrix that
Graph Using represents heights on an evenly spaced grid. For more information
hist2d about persp, see the section Perspective Plots in the Application
Developer’s Guide.
To create a sample persp graph using hist2d to preprocess the data,
in the Commands window, type the following:

persp(hist2d(fuel.bd$Weight, fuel.bd$Mileage))
99
The persp graph is displayed as follows:
Figure 3.33: Graph using hist2d to create a perspective plot
Hint
Using persp of interp might produce a more attractive graph.
Create a Pie A pie chart shows the share of individual values in a variable, relative
Chart to the sum total of all the values. Pie charts display the same
information as bar charts and dot plots, but can be more difficult to
interpret. This is because the size of a pie wedge is relative to a sum,
and does not directly reflect the magnitude of the data value. Because
of this, pie charts are most useful when the emphasis is on an
individual item’s relation to the whole; in these cases, the sizes of the
pie wedges are naturally interpreted as percentages.
Calling pie directly on a big data object can result in a pie with
thousands of wedges; therefore, preprocess the data using table to
reduce the number of wedges.
To create a sample pie chart using table to preprocess the data, in the

pie(table(fuel.bd$Type), names=levels(fuel.bd$Type),
sub="Count")
100
Example Graphs
The pie chart appears as follows:

fif
Figure 3.34: Graph using table to create a pie chart.
Create a Trellis The function piechart creates a pie chart in a Trellis graph.
Pie Chart • If your data contains a small number of cases, convert the
data to a standard data.frame before calling piechart.
• If your data contains a large number of cases, first use
aggregate, and then use bd.coerce to create the appropriate
small data set.
To create a sample Trellis pie chart using aggregate to preprocess the

list(year=barley.bd$year, variety=barley.bd$variety),
sum))
piechart(variety ~ x | year, data = temp.df,
xlab = "Barley Yield (bushels/acre)")
101
The Trellis pie chart appears as follows:
Figure 3.35: Graph using aggregate to create a Trellis pie chart.
Create a Trellis A surface plot is an approximation to the shape of a three-

Wireframe Plot dimensional data set. Surface plots are used to display data collected
on a regularly-spaced grid; if gridded data is not available,
interpolation is used to fit and plot the surface. The Trellis function
that displays surface plots is wireframe.
For big data sets, wireframe requires a preprocessing function such as
loess.
To create a sample Trellis surface plot using loess to preprocess the


{
wind * temperature * radiation, data = environ.bd,
102
Example Graphs
print(wireframe(fit ~ wind * temperature | radiation,

}
The surface plot is displayed as follows:
Figure 3.36: Graph using loess to create a surface plot.
Unsupported Using the functions that add to a plot, such as points and lines,
Functions results in an error message.
103
104
ADVANCED PROGRAMMING
INFORMATION
4
Introduction 106
Big Data Block Size Issues 107
Block Size Options 107
Group or Window Blocks 110
Big Data String and Factor Issues 113
String Column Widths 113
String Widths and importData 113
String Widths and bd.create.columns 115
Factor Column Levels 116
String Truncation and Level Overflow Errors 117
Storing and Retrieving Large S Objects 119
Managing Large Amounts of Data 119
Increasing Efficiency 121
bd.select.rows 121
bd.filter.rows 121
bd.create.columns 122
105
Chapter 4 Advanced Programming Information
INTRODUCTION
As an S-PLUS Big Data library user, you might encounter unexpected
or unusual behavior when you manipulate blocks of data or work
with strings and factors.
This section includes warnings and advice about such behavior, and
provides examples and further information for handling these
unusual situations.
Alternatively, you might need to implement your own big-data
algorithms using out-of-memory techniques.
106
Big Data Block Size Issues
BIG DATA BLOCK SIZE ISSUES

Big data objects represent very large amounts of data by storing the
data in external files. When a big data object is processed, pieces of
this data are read into memory and processed as data “blocks.” For
most operations, this happens automatically. This section describes
situations where you might need to understand the processing of
individual blocks.
Block Size When processing big data, the system must decide how much data to
Options read and process in each block. Each block should be as big as
possible, because it is more efficient to process a few large blocks,
rather than many small blocks. However, the available memory limits
the block size. If space is allocated for a block that is larger than the
physical memory on the computer, either it uses virtual memory to
store the block (which slows all operations), or the memory allocation
operation fails.
The size of the blocks used is controlled by two options:
• bd.options("block.size")
The option "block.size" specifies the maximum number of
rows to be processed at a time, when executing big data
operations. The default value is 1e9; however, the actual
number of rows processed is determined by this value,
adjusted downwards to fit within the value specified by the
option "max.block.mb".
• bd.options("max.block.mb")
The option "max.block.mb" places a limit on the maximum
size of the block in megabytes. The default value is 10.
When S-PLUS reads a given bdFrame, it sets the block size initially to
the value passed in "block.size", and then adjusts downward until
the block size is no greater than "max.block.mb". Because the default
for "block.size" is set so high, this effectively ensures that the size of
the block is around the given number of megabytes.
The resulting number of rows in a block depends on the types and
numbers of columns in the data. Given the default "max.block.mb" of
10 megabytes, reading a bdFrame with a single numeric column could
107
be read in blocks of 1,250,000 rows. A bdFrame with 200 numeric

columns could be read in blocks of 6,250 rows. The column types
also enter into the determination of the number of rows in a block.
Changing Block There is rarely a reason to change bd.options("block.size") or

Size Options bd.options("max.block.mb"). The default values work well in almost
all situations. In this section, we examine possible reasons for
changing these values.
A bad reason for changing the block size options is to guarantee a
particular block size. For example, one might set
bd.options("block.size") to 50 before calling bd.block.apply with
its FUN argument set to a function that depends on receiving blocks of
exactly 50 rows. Writing functions that depend on a specific number
of rows is strongly discouraged, because there are so many situations
where this function might fail, including:
• If the whole dataset is not a multiple of 50 rows, then the last
block will have fewer than 50 rows.
• If the dataset being processed has a large number of columns,
then the actual rows in each block will be less than 50 (if
bd.options("max.block.mb") is too small), or an out of
memory error might occur when allocating the block (if
bd.options("max.block.mb") is too high). If it is necessary to
guarantee 50-row blocks, it would be better to call
bd.by.window with window=50, offset=0, and
drop.incomplete=T.
A good reason for changing bd.options("block.size") is if you are

developing and debugging new code for processing big data.
Consider developing code that calls bd.block.apply to processes
very large data in a series of chunks. To test whether this code works
when the data is broken into multiple blocks, set "block.size" to a
very small value, such as bd.options(block.size=10). Test it with
several small values of bd.options("block.size") to ensure that it
does not depend on the block size. Using this technique, you can test
processing multiple blocks quickly with very small data sets.
One situation where it might be necessary to increase
bd.options("max.block.mb") is when you use bd.by.group or
bd.by.window. These functions call an S-PLUS function on each data
108
block defined by the group columns or the window size, and it will
generate an error if a data block is larger than
bd.options("max.block.mb").
You can work around this problem by increasing

bd.options("max.block.mb"), but you run the risk of an out of
memory error. If the number of groups is not large, it would be better
to call bd.split.by.group or bd.split.by.window to divide the
dataset into separate datasets for each group, and then process them
individually. The section Group or Window Blocks on page 110
contains an example.
A common reason for increasing bd.options("block.size") or
bd.options("max.block.mb") is to attempt to improve performance.
Most of the time this is not effective. While it is often faster to process
a few large blocks than many small blocks, this does not mean that
the best way to improve performance is to set the block size as high as
possible.
With very small block sizes, a lot of time can go into the overhead of
reading and writing and managing the individual blocks. As the block
sizes get larger, this overhead gets lower relative to the other
processing. Eventually, increasing the block size will not make much
difference. This is shown in Figure 4.1, where the time for calling
bd.block.apply on a large data set is measured for different values of
bd.options("max.block.mb").
bd.options("block.size") is set to the default of 1e9 in all cases, so

the actual block size used is determined by
bd.options("max.block.mb"). The different symbols show
109
measurements with four different FUN functions. All of the symbols

show the same trend: Increasing the block size improves the
performance for a while, but eventually the improvement levels out.
Figure 4.1: Efficiency of setting bd.options(“max.block.mb”).
If you suspect that increasing the block size could help the
performance of a particular computation, the best strategy is to
measure the performance of the computation with
bd.options("max.block.mb") set to the default of 10, and then
measure it again with bd.options("max.block.mb") set to 20. If this
test shows no significant performance improvement, it probably will
not help to increase the block size further, but could lead only to out
of memory problems. Using large block sizes can actually lead to
worse performance, if it causes virtual memory page swapping.
Group or Note that the “block” size determined by these options and the data is
Window Blocks distinct from the “blocks” defined in the functions bd.by.group,
bd.by.window, bd.split.by.group, and bd.split.by.window. These
functions divide their input data into subsets to process as determined
by the values in certain columns or a moving window. S-PLUS
imposes a limit on the size of the data that can be processed in each
block by bd.by.group and bd.by.window: if the number of rows in a
block is larger than the block size determined by
110
bd.options("block.size") and bd.options("max.block.mb"), an

error is displayed. This limitation does not apply to the functions
bd.split.by.group and bd.split.by.window.
To demonstrate this restriction, consider the code below. The

variable BIG.GROUPS contains a 1,000-row data.frame with a column
GENDER with factor values MALE and FEMALE, split evenly between the
rows. If the block size is large enough, we can use bd.by.group to
process each of the GENDER groups of 500 rows:
BIG.GROUPS <-
data.frame(GENDER=rep(c("MALE","FEMALE"),
length=1000), NUM=rnorm(1000))
bd.options(block.size=5000)
bd.by.group(BIG.GROUPS, by.columns="GENDER",
FUN=function(df)
data.frame(GENDER=df$GENDER[1],
NROW=nrow(df)))
GENDER NROW
1 FEMALE 500
2 MALE 500
If the block size is set below the size of the groups, this same
operation will generate an error:
bd.options(block.size=10)
bd.by.group(BIG.GROUPS, by.columns="GENDER",
FUN=function(df)
data.frame(GENDER=df$GENDER[1],
NROW=nrow(df)))
Problem in bd.internal.exec.node(engine.class = :
BDLManager$BDLSplusScriptEngineNode (0): Problem in
bd.internal.by.group.script(IM, function(..: can't process
block with 500 rows for group [FEMALE]: can only process 10
rows at a time (check bd.options() values for block.size
and max.block.mb)
Use traceback() to see the call stack
In this case, bd.split.by.group could be called to divide the data

into a list of multiple bdFrame objects and process them individually:
111
BIG.GROUPS.LIST <- bd.split.by.group(BIG.GROUPS,

by.columns="GENDER")
data.frame(GENDER=names(BIG.GROUPS.LIST),
NROW=sapply(BIG.GROUPS.LIST, nrow, simplify=T),
row.names=NULL)
GENDER NROW
1 FEMALE 500
2 MALE 500
112
Big Data String and Factor Issues
BIG DATA STRING AND FACTOR ISSUES

Big data columns of types character and factor have limitations that
are not present for regular data.frame objects. Most of the time, these
limitations do not cause problems, but in some situations, warning
messages can appear, indicating that long strings have been
truncated, or factors with too many levels had some values changed
to NA. This section explains why these warnings may appear, and how
to deal with them.
String Column When a bdFrame character column is initially defined, before any data
Widths is stored in it, the maximum number of characters (or string width)
that can appear in the column must be specified. This restriction is
necessary for rapid access to the cache file. Once this is specified, an
attempt to store a longer string in the column causes the string to be
truncated and generate a warning. It is important to specify this
maximum string width correctly. All of the big data operations
attempt to estimate this width, but there are situations where this
estimated value is incorrect. In these cases, it is possible to explicitly
specify the column string width.
To retrieve the actual column string widths used in a particular
bdFrame, call the function bd.string.column.width.
Unless the column string width is explicitly specified in other ways,
the default string width for newly-created columns is set with the
following option. The default value is 32.
bd.options("string.column.width")
When you convert a data.frame with a character column to a

bdFrame, the maximum string width in the column data is used to set
the bdFrame column string width, so there is no possibility of string
truncation.
String Widths When you import a big data object using importData for file types
and other than ASCII text, S-PLUS determines the maximum number of
characters in each string column and uses this value to set the bdFrame
importData
column string width.
113
When you import ASCII text files, S-PLUS measures the maximum
number of characters in each column while scanning the file to
determine the column types. The number of lines scanned is
controlled by the argument scanLines. If this is too small, and the
scan stops before some very long strings, it is possible for the
estimated column width to be too low. For example, the following
code generates a file with steadily-longer strings.
f <- tempfile()
cat("strsize,str\n",file=f)
for(x in 1:30) {
str <- paste(rep("abcd:",x),collapse="")
cat(nchar(str), ",", str, "\n", sep="",
append=T, file=f)
}
Importing this file with the default scanLines value (256) detects that
the maximum string has 150 characters, and sets this column string
length correctly.
dat <- importData(f, type="ASCII", stringsAsFactors=F,

bigdata=T)
dat
**bdFrame: 30 rows, 2 columns**

strsize str
1 5 abcd:
2 10 abcd:abcd:
3 15 abcd:abcd:abcd:
4 20 abcd:abcd:abcd:abcd:
5 25 abcd:abcd:abcd:abcd:abcd:
... 25 more rows ...
bd.string.column.width(dat)
strsize str
-1 150
(In the above output, the strsize value of -1 represents the value for
non-character columns.)
If you import this file with the scanLines argument set to scan only
the first few lines, the column string width is set too low. In this case,
the column string width is set to 45 characters, so longer strings are
truncated, and a warning is generated:
114

bigdata=T, scanLines=10)
Warning messages:
"ReadTextFileEngineNode (0): output column str has 21
string values truncated because they were longer than the
column string width of 45 characters -- maximum string size
before truncation was 150 characters" in:
bd.internal.exec.node(engine.class = engine.class, ...
You can read this data correctly without scanning the entire file by
explicitly setting bd.options("default.string.column.width")
before the call to importData:
bd.options("default.string.column.width"=200)
bigdata=T, scanLines=10)
bd.string.column.width(dat)
strsize str
-1 200
This string truncation does not occur when S-PLUS reads long strings
as factors, because there is no limit on factor-level string length.
One more point to remember when you import strings: the low-level
importData and exportData code truncates any strings (either
character strings or factor levels) that have more than 254 characters.
S-PLUS generates a warning in importData if bigdata=T if it
encounters such strings.
String Widths You can use one of the following techniques for setting string column
and widths explicitly:
bd.create. • To set the default width (if it is not determined some other
columns way), use bd.options("string.column.width").
• To override the default column string widths, in
bd.block.apply, specify the out1.column.string.widths list
element when IM$test==T, or when outputting the first non-
NULL output block.
• To set the width for new output columns, use the

string.column.width argument to bd.create.columns.
When you use bd.create.columns to create a new character
column, you must set the column string width. You can set
115
this width explicitly with the string.column.width argument.

If you set it smaller than the maximum string generated, then
this will generate a warning:
bd.create.columns(as.bdFrame(fuel.frame),
"Type+Type", "t2", "character",
string.column.width=6)
Warning in bd.internal.exec.node(engine.class = engi..:

"CreateColumnsEngineNode (0): output column t2 has 53
string values truncated because they were longer than the
column string width of 6 characters -- maximum string size
before truncation was 14 characters"
**bdFrame: 60 rows, 6 columns**

Weight Disp. Mileage Fuel Type t2
1 2560 97 33 3.030303 Small SmallS
2 2345 114 33 3.030303 Small SmallS
3 1845 81 37 2.702703 Small SmallS
4 2260 91 32 3.125000 Small SmallS
5 2440 113 32 3.125000 Small SmallS
... 55 more rows ...
If the character column width is not set with the

string.column.width argument, the value is estimated differently,
depending on whether the call.splus argument is true or false. If
row.language=T, the expression is analyzed to determine the
maximum length string that could possibly be generated. This
estimate is not perfect, but it works well enough most of the time.
If row.language=F, the first time that the S-PLUS expression is
evaluated, the string widths are measured, and the new column's
string width is set from this value. If future evaluations produce longer
strings, they are truncated, and a warning is generated.
Whether row.language=T or F, the estimated string widths will never
be less than the value of
bd.options("default.string.column.width").
Factor Column Because of the way that bdFrame factor columns are represented, a
Levels factor cannot have an unlimited number of levels. The number of
levels is restricted to the value of the option. (The default is 500.)
bd.options("max.levels")
116
If you attempt to create a factor with more than this many levels, a
warning is generated. For example:
dat <- bd.create.columns(data.frame(num=1:2000),

"'x'+num", "f", "factor")
Warning messages:
"CreateColumnsEngineNode (0): output column f has 1500 NA
values due to categorical level overflow (more than 500
levels) -- you may want to change this column type from
categorical to string" in: bd.internal.ex\
ec.node(engine.class = engine.class, node.props =
node.props, ....
summary(dat)
num f
Min.: 1.0 x99: 1
1st Qu.: 500.8 x98: 1
Median: 1001.0 x97: 1
Mean: 1001.0 x96: 1
3rd Qu.: 1500.0 x95: 1
Max.: 2000.0 (Other): 495
NA's:1500
You can increase the "max.levels" option up to 65,534, but factors

with so many levels should probably be represented as character
strings instead.
Note
Strings are used for identifiers (such as street addresses or social security numbers), while factors
are used when you have a limited number of categories (such as state names or product types)
that are used to group rows for tables, models, or graphs.
String Normally, if strings are truncated or factor levels overflow, S-PLUS

Truncation and displays a warning with detailed information on the number of
altered values after the operation is completed. You can set the
Level Overflow following options to make an error occur immediately when a string
Errors truncation or level overflow occurs.
bd.options("error.on.string.truncation"=T)
bd.options("error.on.level.overflow"=T)
117
The default for both options is F. If one of these is set to T, an error

occurs, with a short error message. Because all of the data has not
been processed, it is impossible to determine how many values might
be effected.
These options are useful in situations where you are performing a
lengthy operation, such as importing a huge data set, and you want to
terminate it immediately if there is a possible problem.
118
Storing and Retrieving Large S Objects
STORING AND RETRIEVING LARGE S OBJECTS

When you work with very large data, you might encounter a situation
where an object or collection of objects is too large to fit into available
memory. The Big Data library offers two functions to manage storing
and retrieving large data objects:
• bd.pack.object
• bd.unpack.object
This topic contains examples of using these functions.
Managing Suppose you want to create a list containing thousands of model

Large Amounts objects, and a single list containing all of the models is too large to fit
in your available memory. By using the function bd.pack.object,
of Data you can store each model in an external cache, and create a list of the
smaller “packed” models. You can then use bd.unpack.object to
restore the models to manipulate them.
Creating a In the following example, use the data object fuel.frame to create
Packed Object 1000 linear models. The resulting object takes about 6MB.
with bd.pack. In the Commands window, type the following:
object
#Create the linear models:
many.models <- lapply(1:1000, function(x)
lm(Fuel ~ Weight + Disp., sample(fuel.frame, size=30)))
#Get the size of the object:

object.size(many.models)
[1] 6210981
You can make a smaller object by packing each model. While this
exercise takes longer, the resulting object is smaller than 2MB.
In the Commands window, type the following:
#Create the packed linear models:

many.models.packed <- lapply(1:1000,
function(x) bd.pack.object(
lm(Fuel ~ Weight + Disp., sample(fuel.frame, size=30))))
119
#Get the size of the packed object:

object.size(many.models.packed)
[1] 1880041
Restoring a Remember if you use bd.pack.object, you must unpack the object to
Packed Object use it again. The following example code unpacks some of the models
with within many.models.packed object and displays them in a plot.
bd.unpack. In the Commands window, type the following:
object
for(x in 1:5)
plot(
bd.unpack.object(many.models.packed[[x]]),
which.plots=3)
Summary The above example shows a space difference of only a few MB, (6MB
to 2MB), which is probably not a large enough saving to take the time
to pack the object. However, if each of the model objects were very
large, and the whole list were too large to represent, the packed
version would be useful.
120
Increasing Efficiency
INCREASING EFFICIENCY
The Big Data library offers several alternatives to standard S-PLUS
functions, to provide greater efficiency when you work with a large
data set. Key efficiency functions include:
Table D.1: Efficient Big Data library functions.
bd.select.rows Use to extract specific columns and a block of

contiguous rows.
bd.filter.rows Use to keep all rows for which a condition is

TRUE.
bd.create.columns Use to add columns to a data set.
The following section provides comparisons between these Big Data

library functions and their standard S-PLUS function equivalents
bd.select. Using bd.select.rows to extract a block of rows is much more

rows efficient than using standard subscripting. Some standard subscripting
and bd.select.rows equivalents include the following:.
Table D.2: bd.select.rows efficiency equivalents.
Standard S-PLUS subscripting

function bd.select.rows equivalent
x[, "Weight"] bd.select.rows(x,

columns="Weight")
x[1:1000, c(1,3)] bd.select.rows(x, from=1, to=1000,

columns=c(1,3))
bd.filter. Using bd.filter.rows is equivalent to subscripting rows with a

rows logical vector. By default, bd.filter.rows uses an “expression
language” that provides quick evaluation of row-oriented expressions.
Alternatively, you can use the full range of S-PLUS row functions by
121
setting the bd.filter.rows argument row.language=F, but the

computation is less efficient. Some standard subscripting and
bd.filter.rows equivalents include the following:.
Table D.3: bd.filter.rows efficiency equivalents.

function bd.filter.rows equivalent
x[x$Weight > 100, ] bd.filter.rows(x, "Weight > 100")
x[pnorm(x$stat) > 0.5 ,] bd.filter.rows(x, "pnorm(stat) >

0.5", row.language=F)
bd.create. Like bd.filter.rows, bd.create.columns offers you a choice of using

columns the more efficient expression language or the more flexible general
S-PLUS functions. Some standard subscripting and
bd.create.columns equivalents include the following:
Table D.4: bd.create.columns efficiency equivalents.

function bd.create.columns equivalent
x$d <- (x$a+x$b)/x$c x <- bd.create.columns(x, "(a+b)/

c", "d")
x$pval <- pnorm(x$stat) x <- bd.create.columns(x,

"pnorm(stat)", "pval",
row.language=F)
y <- (x$a+x$b)/x$c y <- bd.create.columns(x, "(a+b)/

c", "d", copy=F)
Note that in the last function, above, specifying copy=F creates a new
column without copying the old columns.
122
APPENDIX: BIG DATA
LIBRARY FUNCTIONS
Introduction 124
Data Import and Export 125
Object Creation 126
Big Vector Generation 127
Data Frame and Vector Functions 136
Graph Functions 150
Data Modeling 152
Time Date and Series Functions 156
123
Appendix: Big Data Library Functions
INTRODUCTION
The Big Data library is supported by many standard S-PLUS
functions, such as basic statistical and mathematical functions,
properties functions, densities and quantiles functions, and so on. For
more information about these functions, see their individual help
topics. (To display a function’s help topic, in the Commands window,
type help(functionname).)
The Big Data library also contains functions specific to big data
objects. These functions include the following.
• Import and export functions.
• Object creation functions
• Big vector generating functions.
• Data exploration and manipulation functions.
• Traditional and Trellis graphics functions.
• Modeling functions.
These functions are described further in the following section.
124
Big Data Library Functions
BIG DATA LIBRARY FUNCTIONS

The following tables list the functions that are implemented in the Big
Data library.
Data Import For more information and usage examples, see the functions’
and Export individual help topics.
Table A.1: Import and export functions.
data.dump Creates a file containing an ASCII

representation of the objects that are named.
data.restore Puts data objects that had previously been put

into a file with data.dump into the specified
database.
exportData Exports a bdFrame to the specified file or

database format. Not all standard S-PLUS
arguments are available when you import a
large data set. See exportData in the S-PLUS
Language Reference for more information.
importData When you set the bigdata flag to TRUE, imports

data from a file or database into a bdFrame. Not
all standard S-PLUS arguments are available
when you import a large data set. See
importData in the S-PLUS Language Reference
for more information.
125
Object The following methods create an object of the specified type. For
Creation more information and usage examples, see the functions’ individual
help topics.
Table A.2: Big Data library object creation functions
Function
bdCharacter
bdCluster
bdFactor
bdFrame
bdGlm
bdLm
bdLogical
bdNumeric
bdPrincomp
bdSignalSeries
bdTimeDate
bdTimeSeries
bdTimeSpan
126
Big Vector For the following methods, set the bigdata argument to TRUE to
Generation generate a bdVector. This instruction applies to all functions in this
table. For more information and usage examples, see the functions’
individual help topics.
Table A.3: Vector generation methods for large data sets.
Method name
rbeta
rbinom
rcauchy
rchisq
rep
rexp
rf
rgamma
rgeom
rhyper
rlnorm
rlogis
rmvnorm
rnbinom
rnorm
127
Table A.3: Vector generation methods for large data sets. (Continued)
Method name
rnrange
rpois
rstab
rt
runif
rweibull
rwilcox
Big Data The Big Data library introduces a new set of "bd" functions designed
Library to work efficiently on large data. For best performance, it is important
that you write code minimizing the number of passes through the
Functions data. The Big Data library functions minimize the number of passes
made through the data. Use these functions for the best performance.
For more information and usage examples, see the functions’
individual help topics.
128
Data Exploration
Functions Table A.4: Data exploration functions.
bd.cor Computes correlation or covariances for a data

set. In addition, computes correlations or
covariances between a single column and all
other columns, rather than computing the full
correlation/covariance matrix.
bd.crosstabs Produces a series of tables containing counts for

all combinations of the levels in categorical
variables.
bd.data.viewer Displays the data viewer window, which displays

the input data in a scrollable window, as well as
information about the data columns (names,
types, means, and so on).
bd.univariate Computes a wide variety of univariate statistics. It

computes most of the statistics returned by PROC
UNIVARIATE in SAS.
129
Data
Manipulation Table A.5: Data manipulation functions.
Functions
bd.aggregate Divides a data object into blocks

according to the values of one or
more columns, and then applies
aggregation functions to columns
within each block.
bd.append Appends one data set to a second

data set.
bd.bin Creates new categorical variables

from continuous variables by
splitting the numeric values into a
number of bins. For example, it can
be used to include a continuous age
column as ranges (<18, 18-24, 25-
35, and so on).
bd.block.apply Executes an S-PLUS script on

blocks of data, with options for
reading multiple input datasets and
generating multiple output data
sets, and processing blocks in
different orders.
bd.by.group Apply an arbitrary S-PLUS function

to multiple data blocks within the
input dataset.
bd.by.window Apply an arbitrary S-PLUS function

to multiple data blocks defined by a
moving window over the input
dataset.
bd.coerce Converts an object from a standard

data frame to a bdFrame, or vice
versa.
130
Table A.5: Data manipulation functions. (Continued)
bd.create.columns Creates columns based on

expressions.
bd.duplicated Determine which rows in a dataset

are unique.
bd.filter.columns Removes one or more columns

from a data set.
bd.filter.rows Filters rows that satisfy the

specified expression.
bd.join Creates a composite data set from

two or more data sets. For each
data set, specify a set of key
columns that defines the rows to
combine in the output. Also, for
each data set, specify whether to
output unmatched rows.
bd.modify.columns Changes column names or types.

Can also be used to drop columns.
bd.normalize Centers and scales continuous

variables. Typically, variables are
normalized so that they follow a
standard Gaussian distribution
(means of 0 and standard
deviations of 1).
To do this, bd.normalize subtracts
the mean or median, and then
divides by either the range or
standard deviation.
131
bd.partition Randomly samples the rows of

your data set to partition it into
three subsets for training, testing,
and validating your models.
bd.relational.difference Get differing rows from two input

data sets.
bd.relational.divide Given a Value column and a Group

column, determine which values
belong to a given Membership as
defined by a set of Group values.
bd.relational.intersection Join two input data sets, ignoring all

unmatched columns, with the
common columns acting as key
columns.
bd.relational.join Join two input data sets with the

common columns acting as key
columns.
bd.relational.product Join two input data sets, ignoring all

matched columns, by performing
the cross product of each row.
bd.relational.project Remove one or more columns

from a data set.
bd.relational.restrict Select the rows that satisfy an

expression. Determines whether
each row should be selected by
evaluating the restriction. The
result should be a logical value.
132
bd.relational.union Retrieve the relational union of two

data sets. Takes two inputs (bdFrame
or data.frame). The output
contains the common columns and
includes the rows from both inputs,
with duplicate rows eliminated.
bd.remove.missing Drops rows with missing values, or

replaces missing values with the
column mean, a constant, or values
generated from an empirical
distribution, based on the observed
values.
bd.reorder.columns Changes the order of the columns

in the data set.
bd.sample Samples rows from a dataset, using

one of several methods.
bd.select.rows Extracts a block of data, as

specified by a set of columns, start
row, and end row.
bd.shuffle Randomly shuffles the rows of your

data set, reordering the values in
each of the columns as a result
bd.sort Sorts the data set rows, according

to the values of one or more
columns.
bd.split Splits a data set into two data sets

according to whether each row
satisfies an expression.
133
bd.sql Specifies data manipulation

operations using SQL syntax.
• The Select, Insert,
Delete, and Update
statements are supported.
• The column identifiers are
case sensitive.
• SQL interprets periods in
names as indicating fields
within tables; therefore,
column names should not
contain periods if you plan
to use bd.sql.
• Mathematical functions
are allowed for
aggregation (avg, min,
max, sum, count, stdev,
var).
The following functionality is not
implemented:
• distinct
• mathematical functions in
set or select, such as abs,
round, floor, and so on.
• natural join
• union
• merge
• between
• subqueries
bd.stack Combines or stacks separate

columns of a data set into a single
column, replicating values in other
columns as necessary.
134
bd.string.column.width Returns the maximum number of

characters that can be stored in a
big data string column.
bd.transpose Turns a set of columns into a set of

rows.
bd.unique Remove all duplicated rows from

the dataset so that each row is
guaranteed to be unique.
bd.unstack Separates one column into a

number of columns based on a
grouping column.
Programming
Table A.6: Programming functions.
bd.cache.cleanup Cleans up cache files that have not

been deleted by the garbage
collection system. (This is most
likely to occur if the entire system
crashes.)
bd.cache.info Analyzes a directory containing big

data cache files and returns
information about cache files,
references counts, and unknown
files.
bd.options Controls S-PLUS options used

when processing big data objects.
bd.pack.object Packs any object into an external

cache.
135
Table A.6: Programming functions. (Continued)
bd.split.by.group Divide a dataset into multiple data

blocks, and return a list of these
data blocks.
bd.split.by.window Divide a dataset into multiple data

blocks, defined by a moving
window over the dataset, and
return a list of these data blocks.
bd.unpack.object Unpacks a bdPackedObject object

that was previously stored in the
cache using bd.pack.object.
Data Frame The following table lists the functions for both data frames (bdFrame)
and Vector and vectors (bdVector). The the cross-hatch (#) indicates that the
function is implemented for the corresponding object type. The
Functions Comment column provides information about the function, or
indicates which bdVector-derived class(es) the function applies to. For
more information and usage examples, see the functions’ individual
help topics.
Table A.7: Functions implemented for bdVector and bdFrame.
Function Name bdVector bdFrame Optional Comment
- # #
!= # #
$ #
$<- #
[ # #
[[ # #
136
Table A.7: Functions implemented for bdVector and bdFrame. (Continued)
[[<- # #
[<- # #
abs #
aggregate # #
all # #
all.equal # #
any # #
anyMissing # #
append #
apply #
Arith # #
as.bdCharacter #
as.bdFactor #
as.bdFrame # #
as.bdLogical # Handles all bdVector-

derived object types.
as.bdVector # #
attr # #
137
attr<- # #
attributes # #
attributes<- # #
bdFrame # # Constructor. Inputs

can be bdVectors,
bdFrames, or ordinary
objects.
boxplot # # Handles bdNumeric.
by #
casefold #
ceiling #
coerce # #
colIds #
colIds<- #
colMaxs # #
colMeans # #
colMins # #
colRanges # #
colSums # #
138
colVars # #
concat.two # #
cor # #
cut #
dbeta # Density, cumulative

distribution (CDF),
and quantile function.
dbinom # Density, CDF, and

quantile function.
dcauchy # Density, CDF, and

quantile function.
dchisq # Density, CDF, and

quantile function.
density #
densityplot #
dexp # Density, CDF, and

quantile function.
df # Density, CDF, and

quantile function.
dgamma # Density, CDF, and

quantile function.
dgeom # Density, CDF, and

quantile function.
139
dhyper # Density, CDF, and

quantile function.
diff # #
digamma #
dim #
dimnames # a bdFrame has no row

names.
dimnames<- # a bdFrame has no row

names.
dlnorm # Density, CDF, and

quantile function.
dlogis # Density, CDF, and

quantile function.
dmvnorm # Density and CDF

function.
dnbinom # Density, CDF, and

quantile function.
dnorm # Density, CDF, and

quantile function.
dnrange # Density, CDF, and

quantile function.
dpois # Density, CDF, and

quantile function.
140
dt # Density, CDF, and

quantile function.
dunif # Density, CDF, and

quantile function.
duplicated # # Density, CDF, and

quantile function.
durbinWatson # Density, CDF, and

quantile function.
dweibull # Density, CDF, and

quantile function.
dwilcox # Density, CDF, and

quantile function.
floor # #
format # #
formula #
grep #
hist #
hist2d #
histogram #
html.table # #
intersect #
141
is.all.white #
is.element #
is.finite # #
is.infinite # #
is.na # #
is.nan # #
is.number # #
is.rectangular # #
kurtosis # Handles bdNumeric.
length # #
levels # Handles bdFactor.
levels<- # Handles bdFactor.
mad #
match # #
Math # # Operand function.
Math2 # # Operand function.
matrix # #
142
mean # #
median #
merge # #
na.exclude # #
na.omit # #
names # # bdVector cannot have

names.
names<- # # bdVector cannot have

names.
nchar # Handles bdCharacter,

not bdFactor.
ncol #
notSorted #
nrow #
numberMissing # #
Ops # #
pairs #
pbeta # Density, CDF, and

quantile function.
143
pbinom # Density, CDF, and

quantile function.
pcauchy # Density, CDF, and

quantile function.
pchisq # Density, CDF, and

quantile function.
pexp # Density, CDF, and

quantile function.
pf # Density, CDF, and

quantile function.
pgamma # Density, CDF, and

quantile function.
pgeom # Density, CDF, and

quantile function.
phyper # Density, CDF, and

quantile function.
plnorm # Density, CDF, and

quantile function.
plogis # Density, CDF, and

quantile function.
plot # #
pmatch #
pmvnorm # Density and CDF

function.
144
pnbinom # Density, CDF, and

quantile function.
pnorm # Density, CDF, and

quantile function.
pnrange # Density, CDF, and

quantile function.
ppois # Density, CDF, and

quantile function.
print # #
pt # Density, CDF, and

quantile function.
punif # Density, CDF, and

quantile function.
pweibull # Density, CDF, and

quantile function.
pwilcox # Density, CDF, and

quantile function.
qbeta # Density, CDF, and

quantile function.
qbinom # Density, CDF, and

quantile function.
qcauchy # Density, CDF, and

quantile function.
145
qchisq # Density, CDF, and

quantile function.
qexp # Density, CDF, and

quantile function.
qf # Density, CDF, and

quantile function.
qgamma # Density, CDF, and

quantile function.
qgeom # Density, CDF, and

quantile function.
qhyper # Density, CDF, and

quantile function.
qlnorm # Density, CDF, and

quantile function.
qlogis # Density, CDF, and

quantile function.
qnbinom # Density, CDF, and

quantile function.
qnorm # Density, CDF, and

quantile function.
qnrange # Density, CDF, and

quantile function.
qpois # Density, CDF, and

quantile function.
146
qq #
qqmath #
qqnorm #
qqplot #
qt # Density, CDF, and

quantile function.
quantile #
qunif # Density, CDF, and

quantile function.
qweibull # Density, CDF, and

quantile function.
qwilcox # Density, CDF, and

quantile function.
range #
rank #
replace #
rev # #
rle #
row.names # Always NULL.
row.names<- # Does nothing.
147
rowIds # Always NULL.
rowIds<- # Does nothing.
rowMaxs #
rowMeans #
rowMins #
rowRanges #
rowSums #
rowVars #
runif #
sample # #
scale #
setdiff #
shiftPositions #
show # #
skewness # Handles bdNumeric.
sort #
split #
148
stdev # Handles
bdCharacter.
sub # #
sub<- #
substring #
substring<- #
Summary # # Operand function.
summary # #
sweep #
t #
tabulate # Handles bdNumeric.
tapply # #
trigamma #
union #
unique # #
var # #
which.infinite # #
which.na # #
149
which.nan # #
xy2cell #
xyCall #
xyplot #
Graph For more information and examples for using the traditional graph
Functions functions, see their individual help topics, or see the section Functions
Supporting Graphs on page 63.
Table A.8: Traditional graph functions.
Function name
barplot
boxplot
contour
dotchart
hexbin
hist
hist2d
image
interp
pairs
150
Table A.8: Traditional graph functions. (Continued)
Function name
persp
pie
plot
qqnorm
qqplot
For more information about using the Trellis graph functions, see their
individual help topics, or see the section Functions Supporting
Graphs on page 63.
Table A.9: Trellis graph functions.
Function name
barchart
contourplot
densityplot
dotplot
histogram
levelplot
piechart
qq
151
Note
The cloud and parallel graphics functions are not implemented for bdFrames.
Data Modeling For more information and usage examples, see the functions’ individual
help topics.
Table A.10: Fitting functions
Function name
bdCluster
bdGlm
bdLm
bdPrincomp
Table A.11: Other modeling utilities.
Function name
bd.model.frame.and.matrix
bs
ns
spline.des
contrasts
contrasts<-
152
Model Methods The following table identifies functions implemented for generalized
linear modeling, linear regression, principal components modeling,
and clustering. The cross-hatch (#) indicates the function is
implemented for the corresponding modeling type.
Table A.12: Modeling and Clustering Functions.
principal
Generalized linear Linear components
Function name modeling (bdGlm) Regression (bdLm) (bdPrincomp) bdCluster
AIC #
all.equal #
anova # #
BIC #
coef # #
deviance # #
durbinWatson #
effects #
family # #
fitted # # # #
formula # #
kappa #
labels #
loadings #
153
Table A.12: Modeling and Clustering Functions. (Continued)
principal
Generalized linear Linear components
Function name modeling (bdGlm) Regression (bdLm) (bdPrincomp) bdCluster
logLik #
model.frame #
model.matrix #
plot # #
predict # # # #
print # # # #
print.summary # # #
qqnorm # #
residuals # #
screeplot #
step # #
summary # # #
154
Predict from This table lists the small data models that support the predict
Small Data function. For more information and usage examples, see the functions’
Models individual help topics.
Table A.13: Predicting from small data models.
Small data model using predict

function
arima.mle
bs
censorReg
coxph
coxph.penal
discrim
factanal
gam
glm
gls
gnls
lm
lme
lmList
lmRobMM
loess
loess.smooth
155
Table A.13: Predicting from small data models. (Continued)
Small data model using predict

function
mlm
nlme
nls
ns
princomp
safe.predict.gam
smooth.spline
smooth.spline.fit
survreg
survReg
survReg.penal
tree
Time Date and The following tables include time date creation functions and
Series functions for manipulating time and date, time span, time series, and
signal series objects.
Functions
156
Time Date
Creation Table A.14: Time date creation functions.
bdTimeDate The object constructor.

Note that when you call the
timeDate function with any big
data arguments, then a bdTimeDate
object is created.
timeCalendar Standard S-PLUS function. When

you call the timeCalendar function
with any big data arguments, then
a bdTimeDate object is created
timeSeq Standard S-PLUS function; to use

with a large data set, set the
bigdata argument to TRUE.
In the following table, the cross-hatch (#) indicates that the function is
implemented for the corresponding class. If the table cell is blank, the
function is not implemented for the class. This list includes bdVector
objects (bdTimeDate and bdTimeSpan) and bdSeries classes
(bdSignalSeries, bdTimeSeries).
Table A.15: Time Date and Series Functions.
Function bdTimeDate bdTimeSpan bdSignalSeries bdTimeSeries
- # #
[ # # #
[<- #
+ # #
align # #
157
Table A.15: Time Date and Series Functions. (Continued)
all.equal # #
Arith # #
as.bdFrame # # #
as.bdLogical # #
bd.coerce # # # #
ceiling # #
coerce/as # # # #
cor # # # #
cumsum #
cut # #
data.frameAux # # #
days #
deltat # #
diff # #
end # #
floor # #
hms #
158
hours #
match # #
Math # # # #
Math2 # # # #
max # #
mdy #
mean # # # #
median # # # #
min # #
minutes #
months #
plot # # # #
quantile # # # #
quarters #
range # #
seconds #
seriesLag # #
159
shiftPositions # #
show # # # #
sort # # # #
sort.list # # # #
split # #
start # #
substring<- # # # #
sum #
Summary # # # #
summary # # # #
timeConvert #
trunc # #
var # # # #
wdydy #
weekdays #
yeardays #
years #
160
INDEX
Symbols as.bdFrame 137, 158

as.bdLogical 137, 158
137, 157
as.bdVector 137
!= function 136
attr 137, 138
$ 136
attributes 138, 138
$ function 136
+ function 157
137, 136 B
barchart 67, 90, 151
Numerics barplot 67, 150
basic algebra 18
64-bit 5
bd.aggregate 9, 47, 130
bd.append 130
A bd.bin 130
abline 64, 75 bd.block.apply 9, 49, 50, 52, 108,
abs 59, 137 130
aggregate 16, 66, 137 bd.by.group 9, 108, 110, 130
aggregation 130 bd.by.window 10, 110, 130
AIC 153 bd.by.window. 108
algebra 18 bd.cache.cleanup 135
align 157 bd.cache.info 135
all 137 bd.coerce 52, 130, 158
all.equal 137, 153, 158 bd.cor 129
anova 13, 153 bd.create.columns 38, 39, 115, 121,
any 137 122, 131
anyMissing 137 bd.crosstabs 129
append 137 bd.data.viewer 25, 129
appending data sets 130 bd.duplicated 131
apply 137 bd.filter.columns 131
arima.mle 155 bd.filter.rows 29, 30, 121, 122, 131
Arith 137, 158 bd.join 46, 131
as.bdCharacter 137 bd.model.frame.and.matrix 152
as.bdFactor 137 bd.modify.columns 131
161
Index
bd.normalize 131 bdSignalSeries 4, 11, 14, 17, 126

bd.options 8, 12, 107, 135 bdTimeDate 4, 11, 17, 126, 157
bd.pack.object 119, 120, 135 bdTimeSeries 4, 11, 14, 17, 126
bd.partition 132 bdTimeSpan 4, 11, 17, 126
bd.relational.difference 132 bdVector 11, 12, 15, 136
bd.relational.intersection 132 BIC 153
bd.relational.join 132 bigdata flag 15
bd.relational.product 132 binning 130
bd.relational.project 132 block.size 8
bd.relational.restrict 132 block processing 130
bd.relational.union 133 block size 107
bd.remove.missing 133 box plot 79
bd.reorder.columns 133 boxplot 65, 138, 150
bd.sample 133 bs 152, 155
bd.select 121 bwplot 33, 41, 65, 80
bd.select.rows 121, 133 by 138
bd.shuffle 133
bd.sort 133 C
bd.split 133
bd.split.by.group 10, 110, 136 C 152
bd.split.by.window 10, 110, 136 cache files
bd.sql 134 cleaning 135
bd.stack 37, 134 creating external 135
bd.string.column.width 135 information 135
bd.transpose 135 unpacking 136
bd.unique 135 call 58
bd.univariate 129 casefold 138
bd.unpack.object 119, 136 ceiling 138, 158
bd.unstack 135 censorReg 155
bdCharacter 11, 126 census data 22
bdCluster 11, 13, 46, 126, 152 census data description 22
bdFactor 11, 40, 126 censusDemogr 53
bdFrame 11, 14, 31, 126, 136, 138 census demographics, household
introducing the new data type 4 variables 53
bdGLM 11 changing order of columns 133
bdGlm 13, 57, 126, 152 character 113
bdLM 11 classes
bdLm 13, 16, 126, 152 bdCharacter 14
bdLogical 11, 126 bdCluster 14
bdNumeric 11, 126 bdFactor 14
bdPrincomp 11, 13, 126, 152 bdGlm 14
bdSeries 4, 11, 14 bdLm 14
data 14 bdLogical 14
positions 14 bdNumeric 14
units 14 bdPrincomp 14
162
Index
bdSignalSeries 14 data frame 11

bdTimeDate 14 data frames 11
bdTimeSeries 14 data manipulation functions. 130
bdTimeSpan 14 data preparation
bdVector 14 example 27
cleaning data streaming 4
cache files 135 data types 11
cloud 63, 152 data viewer window 129
clustering 13, 45, 153 Data View page 26
coef 13, 58, 153 days 158
coerce 138 dbeta 139
coerce/as 158 dbinom 139
colIds 138, 138 dcauchy 139
colMaxs 138 dchisq 139
colMeans 32, 45, 138 deltat 158
colMins 138 density 81, 139
colRanges 138 densityplot 65, 139, 151
colSums 138 deviance 153
column dexp 139
creating 131 df 139
columns dgamma 139
modifying 131 dgeom 139
colVars 139 dhyper 140
concat.two 139 diff 140, 158
contour 67, 150 digamma 140
contourplot 67, 93, 151 dim 140
contrasts 152, 152 dimnames 140, 140
converting an object 130 discrim 155
cor 139, 158 dividing
correlation computation 129 multiple data blocks 136
covariances computation 129 dlnorm 140
coxph 155 dlogis 140
coxph.penal 155 dmvnorm 140
crossprod 18 dnbinom 140
cumsum 158 dnorm 140
cut 139, 158 dnrange 140
dotchart 68, 95, 150
D dotplot 68, 97, 151
dpois 140
data dt 141
import and export 15 dunif 141
data.dump 125 duplicated 141
data.frameAux 158 durbinWatson 141, 153
data.restore 24, 125 dweibull 141
data exploration functions 129 dwilcox 141
163
Index
E grep 141
effects 153
efficiency H
bd.filter.rows 29 help 39
end 158 hexagonal binning 16, 64, 69
exportData 125 hexbin 34, 64, 66, 75, 150
exporting data 15 hist 32, 65, 83, 141, 150
Expression Language 38 hist2d 16, 66, 97, 141, 150
ExpressionLanguage 29 histogram 65, 85, 141, 151
exprs 39 hms 158
hours 159
F html.table 141
factanal 155
factor 113 I
factor column levels 116 image 66, 68, 97, 150
family 153 importData 25, 113, 125
filtering importing data 15
columns 131 interp 16, 66, 93, 150
rows 131 intersect 141
filtering columns 131 is.all.white 142
fitted 13, 153 is.element 142
Fitting functions 152 is.finite 142
floor 141, 158 is.infinite 142
format 141 is.na 142
formula 13, 141, 153 is.nan 142
formula operators 17 is.number 142
136, 157 is.rectangular 142
- function 136, 157
J
G
joining
gam 155 data sets 132
generalized linear models 13 datasets 131
get joining data sets 131
cache file information 135
getting
K
maximum number of characters
135 kappa 153
glm 57, 155 kurtosis 142
gls 155
gnls 155 L
graph functions 63, 150
Trellis 151 labels 153
graphics functions 15 least squares line 75, 78
164
Index
length 142 model.matrix 154

levelplot 68, 98, 151 modeling functions 16
levels 40, 142, 142 modeling utilities 152
linear modeling 153 models 11
linear regression 13, 153 months 159
lines 64, 76, 103
lm 13, 155 N
lme 155
lmList 155 na.exclude 143
lmRobMM 155 na.omit 143
loadings 153 names 27, 39, 143, 143
loess 16, 67, 155 nchar 143
loess.smooth 67, 155 ncol 143
Loess smoother 75, 76 nlme 156
log 12, 35 nls 156
logLik 154 notSorted 143
lsfit 67, 75 nrow 143
ns 152, 156
numberMissing 143
M
mad 142 O
match 142, 159
Math 142, 159 object creation functions 126
Math2 142, 159 Ops 143
matrix 18, 142 out-of-memory
matrix operations 18 processing 3
max 159 overflow errors 117
max.block.mb 8, 107
max.convert.bytes 8 P
mdy 159
pairs 64, 69, 70, 143, 150
mean 5, 143, 159
pair-wise scatter plot 71
median 33, 143, 159
panel 64, 65
merge 48, 143
panel.lmline 74
metadata 5
parallel 63, 152
min 159
paste 28
minutes 159
pbeta 143
missing value
pbinom 144
example 26
pcauchy 144
missing values
pchisq 144
filtering for 133
persp 66, 68, 99, 151
mlm 156
pexp 144
model 12
pf 144
training, testing, and validating
pgamma 144
132
pgeom 144
model.frame 154
165
Index
phyper 144 qnorm 146

pie 68, 151 qnrange 146
pie chart 100 qpois 146
piechart 68, 101, 151 qq 65, 85, 147, 151
plnorm 144 qqline 65, 78
plogis 144 qqmath 66, 85, 86, 147
plot 13, 58, 64, 65, 69, 71, 144, 151, qqnorm 66, 85, 87, 147, 151, 154
154, 159 qqplot 66, 75, 85, 88, 147, 151
plotting big data 65 qt 147
pmatch 144 quantile 147, 159
pmvnorm 144 quarters 159
pnbinom 145 qunif 147
pnorm 145 qweibull 147
pnrange 145 qwilcox 147
points 51, 103
ppois 145 R
predict 13, 154
small data models 155 range 5, 147, 159
predict, bdCluster 47 rank 147
principal components analysis 13 rbeta 127
principal components modeling 153 rbinom 127
princomp 156 rcauchy 127
print 12, 145, 154 rchisq 127
print.summary 154 regexpr 30
PROC UNIVARIATE 129 regression line 75
programming functions 135 removing
pt 145 duplicated rows 135
punif 145 removing columns 132
pweibull 145 rep 49, 127
pwilcox 145 replace 147
residuals 13, 154
retrieving relational union 133
Q rev 147
qbeta 145 rexp 127
qbinom 145 rf 127
qcauchy 145 rgamma 127
qchisq 146 rgeom 127
qexp 146 rhyper 127
qf 146 rle 147
qgamma 146 rlnorm 127
qgeom 146 rlogis 127
qhyper 146 rmvnorm 127
qlnorm 146 rnbinom 127
qlogis 146 rnorm 127
qnbinom 146 rnrange 128
166
Index
row.language 30 smooth.spline 156

row.names 147, 147 smooth.spline.fit 156
rowIds 148, 148 smoothing spline 77
rowMaxs 148 smooth spline 75
rowMeans 148 sort 148, 160
rowMins 148 sort.list 160
rowRanges 148 sorting
rowSums 148 rows 133
rowVars 148 spline.des 152
rpois 128 split 148, 160
rstab 128 splitting
rt 128 data sets 133
runif 128, 148 splom 64, 72, 73
rweibull 128 SQL syntax
rwilcox 128 using with S-PLUS 134
stacking
S columns 134
start 160
safe.predict.gam 156 stdev 149
sample 148 step 154
sampling rows 133 string.column.width 115
sapply 31 string column widths 113
scalable algorithms 4, 5 stripplot 66, 89
scale 148 sub 149, 149
scaling continuous variables 131 substring 149, 149, 160
scanLines 114 sum 160
scatter plot 70 Summary 149, 160
scatterplot 44 summary 12, 13, 28, 31, 149, 154,
scatterplot matrix 72 160
screeplot 154 survReg 156
seconds 159 survreg 156
selecting survReg.penal 156
rows 132, 133 sweep 149
seq 28
series 11
seriesLag 159
T
set.seed 47 t 45, 149
setdiff 148 table 16, 67, 91
shiftPositions 148, 160 tabulate 149
show 148, 160 tapply 16, 67, 92, 149
shuffling timeCalendar 17, 157
rows 133 timeConvert 160
signalSeries 13 timeDate 17
skewness 148 positions 13
smooth 67 time date functions 157
167
Index
time operations 17 V
timeSeq 157
var 149, 160
timeSeries 13
vector 11
timeZoneConvert 17
vector generation 127
transposing
vectors 12
columns to rows 135
virtual memory limitations 3
tree 156
Trellis 34
Trellis graph W
creating 65 wdydy 160
Trellis graphic object weekdays 160
creating 64 which.infinite 149
Trellis graphics 33 which.na 149
trigamma 149 which.nan 150
trunc 160 whisker plot 80
types 39 wireframe 68, 102
U X
union 149 xy2cell 150
unique 149 xyCall 150
unique columns xyplot 34, 44, 64, 65, 69, 74, 150
determining 131
units 13
univariate statistics 129 Y
unpacking yeardays 160
cache files 136 years 160
168

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the knowledge to act™

Big Data User’s Guide

Copyright Notice Copyright © 1987-2007, Insightful Corporation. All rights reserved.

Information you need if you... See the...

Are a system administrator or a licensed user and S-PLUS licensing Web

Information you need if you... See the...

Are familiar with the S language and S-PLUS, and Application

Want to download or create S-PLUS packages for Guide to Packages

Are looking for categorized information about Function Guide

Chapter 1 Introduction to the Big Data Library 1

Chapter 2 Census Data Example 21

Chapter 3 Creating Graphical Displays

Chapter 4 Advanced Programming Information 105

Appendix: Big Data Library Functions 123

• To ensure that the library is always loaded on startup, add

WORKING WITH A LARGE DATA SET

Problem in read.table: Unable to obtain requested dynamic

This error occurs because S-PLUS requires the operating system to

refers to the cache file on disk. This out-of-memory design requires

modification in the Big Data library, and only minor modifications

Metadata To optimize performance, S-PLUS stores certain calculated statistics as

that is the primary determinant of efficient operation on large data

Summary By bringing together flexible programming and big-data capability,

THE BIG DATA LIBRARY ARCHITECTURE

bd.option argument Description

block.size The block size (in number of rows), the number

max.convert.bytes The maximum size (in bytes) of the big data

max.block.mb The maximum number of megabytes used for

The function bd.options contains other optional arguments for

Function name Description

bd.aggregate Use bd.aggregate to divide a data object into

bd.block.apply Run an S-PLUS script on blocks of data, with

bd.by.group Apply the specified S-PLUS function to multiple

Table 1.2: Block-based computation functions. (Continued)

Function name Description

bd.by.window Apply the specified S-PLUS function to multiple

bd.split.by.group Divide a dataset into multiple data blocks, and

bd.split.by.window Divide a dataset into multiple data blocks

For a detailed discussion on advanced topics, such as block size issues

Big Data class Data type

bdFrame Data frame

bdVector, bdCharacter, bdFactor, Vector

bdLM, bdGLM, bdPrincomp, bdCluster Models

bdSeries, bdTimeSeries, bdSignalSeries Series

• The print function works differently on a bdFrame object than

• The summary function works differently on a bdFrame object

census.data$adjusted.income <- log(census.data$income -

Models S-PLUS Big Data library provides scalable modeling algorithms to

A model object is available for each of the following statistical

Model Type Model Object

Linear regression bdLm

Generalized linear models bdGlm

Principal Components Analysis bdPrincomp

The Big Data library equivalent is a bdSeries object with two

bdFrame Big data frame

bdLm, bdGlm, bdCluster, bdPrincomp Rich model objects

bdVector Big data vector

bdCharacter, bdFactor, bdLogical, Vector type subclasses

bdTimeSeries, bdSignalSeries Series objects