Apriori Algorithm

Apriori algorithm
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Apriori[1] is an algorithm for frequent item set mining and

association rule learning over relational databases. It proceeds by
identifying the frequent individual items in the database and
extending them to larger and larger item sets as long as those
item sets appear sufficiently often in the database. The frequent
item sets determined by Apriori can be used to determine
association rules which highlight general trends in the database:
this has applications in domains such as market basket analysis.
Overview
The Apriori algorithm was proposed by Agrawal and Srikant in
1994. Apriori is designed to operate on databases containing
transactions (for example, collections of items bought by
customers, or details of a website frequentation or IP
addresses[2]). Other algorithms are designed for finding
association rules in data having no transactions (Winepi and
Minepi), or having no timestamps (DNA sequencing). Each
transaction is seen as a set of items (an itemset). Given a
threshold , the Apriori algorithm identifies the item sets which
are subsets of at least transactions in the database.
Apriori uses a "bottom up" approach, where frequent subsets are

extended one item at a time (a step known as candidate
generation), and groups of candidates are tested against the data.
The algorithm terminates when no further successful extensions
are found.
Apriori uses breadth-first search and a Hash tree structure to

count candidate item sets efficiently. It generates candidate item
sets of length from item sets of length . Then it prunes
the candidates which have an infrequent sub pattern. According
to the downward closure lemma, the candidate set contains all
frequent -length item sets. After that, it scans the transaction
database to determine frequent item sets among the candidates.
The pseudo code for the algorithm is given below for a

transaction database , and a support threshold of . Usual set
theoretic notation is employed, though note that is a multiset.
is the candidate set for level . At each step, the algorithm is
assumed to generate the candidate sets from the large item sets
of the preceding level, heeding the downward closure lemma.
accesses a field of the data structure that represents
candidate set , which is initially assumed to be zero. Many
details are omitted below, usually the most important part of the
implementation is the data structure used for storing the
candidate sets, and counting their frequencies.
Examples
Example 1 …
Consider the following database, where each row is a transaction
and each cell is an individual item of the transaction:
alpha beta epsilon
alpha beta theta
alpha beta epsilon
alpha beta theta
The association rules that can be determined from this database

are the following:
1. 100% of sets with alpha also contain beta

2. 50% of sets with alpha, beta also have epsilon
3. 50% of sets with alpha, beta also have theta
we can also illustrate this through a variety of examples.
Example 2 …
Assume that a large supermarket tracks sales data by stock-

keeping unit (SKU) for each item: each item, such as "butter" or
"bread", is identified by a numerical SKU. The supermarket has a
database of transactions where each transaction is a set of SKUs
that were bought together.
Let the database of transactions consist of following itemsets:

Itemsets
{1,2,3,4}
{1,2,4}
{1,2}
{2,3,4}
{2,3}
{3,4}
{2,4}
We will use Apriori to determine the frequent item sets of this

database. To do this, we will say that an item set is frequent if it
appears in at least 3 transactions of the database: the value 3 is
the support threshold.
The first step of Apriori is to count up the number of occurrences,

called the support, of each member item separately. By scanning
the database for the first time, we obtain the following result
Item Support
{1} 3
{2} 6
{3} 4
{4} 5
All the itemsets of size 1 have a support of at least 3, so they are

all frequent.
The next step is to generate a list of all pairs of the frequent

items.
For example, regarding the pair {1,2}: the first table of Example 2
shows items 1 and 2 appearing together in three of the itemsets;
therefore, we say item {1,2} has support of three.
Item Support
{1,2} 3
{1,3} 1
{1,4} 2
{2,3} 3
{2,4} 4
{3,4} 3
The pairs {1,2}, {2,3}, {2,4}, and {3,4} all meet or exceed the
minimum support of 3, so they are frequent. The pairs {1,3} and
{1,4} are not. Now, because {1,3} and {1,4} are not frequent, any
larger set which contains {1,3} or {1,4} cannot be frequent. In this
way, we can prune sets: we will now look for frequent triples in the
database, but we can already exclude all the triples that contain
one of these two pairs:
Item Support
{2,3,4} 2
in the example, there are no frequent triplets. {2,3,4} is below the

minimal threshold, and the other triplets were excluded because
they were super sets of pairs that were already below the
threshold.
We have thus determined the frequent sets of items in the

database, and illustrated how some items were not counted
because one of their subsets was already known to be below the
threshold.
Limitations
Apriori, while historically significant, suffers from a number of
inefficiencies or trade-offs, which have spawned other algorithms.
Candidate generation generates large numbers of subsets (The
algorithm attempts to load up the candidate set, with as many as
possible subsets before each scan of the database). Bottom-up
subset exploration (essentially a breadth-first traversal of the
subset lattice) finds any maximal subset S only after all
of its proper subsets.
The algorithm scans the database too many times, which reduces
the overall performance. Due to this, the algorithm assumes that
the database is Permanent in the memory.
Also, both the time and space complexity of this algorithm are
very high: , thus exponential, where is the horizontal
width (the total number of items) present in the database.
Later algorithms such as Max-Miner[3] try to identify the maximal

frequent item sets without enumerating their subsets, and
perform "jumps" in the search space rather than a purely bottom-
up approach.
References
1. Rakesh Agrawal and Ramakrishnan Srikant Fast algorithms for
mining association rules . Proceedings of the 20th
International Conference on Very Large Data Bases, VLDB,
pages 487-499, Santiago, Chile, September 1994.
2. The data science behind IP address matching Published by
deductive.com, September 6, 2018, retrieved September 7,
2018
3. Bayardo Jr, Roberto J. (1998). "Efficiently mining long patterns
from databases" (PDF). ACM SIGMOD Record. 27 (2).
External links
ARtool , GPL Java association rule mining application with GUI,
offering implementations of multiple algorithms for discovery
of frequent patterns and extraction of association rules
(includes Apriori)
SPMF offers Java open-source implementations of Apriori and
several variations such as AprioriClose, UApriori, AprioriInverse,
AprioriRare, MSApriori, AprioriTID, and other more efficient
algorithms such as FPGrowth and LCM.
Christian Borgelt provides C implementations for Apriori and
many other frequent pattern mining algorithms (Eclat,
FPGrowth, etc.). The code is distributed as free software under
the MIT license.
The R package arules contains Apriori and Eclat and
infrastructure for representing, manipulating and analyzing
transaction data and patterns.
Efficient-Apriori is a Python package with an implementation of
the algorithm as presented in the original paper.
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title=Apriori_algorithm&oldid=985537784"
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Apriori algorithm

This article needs additional citations for veriﬁcation.

Apriori[1] is an algorithm for frequent item set mining and

Apriori uses a "bottom up" approach, where frequent subsets are

Apriori uses breadth-ﬁrst search and a Hash tree structure to

The pseudo code for the algorithm is given below for a

alpha beta epsilon

alpha beta theta

alpha beta epsilon

alpha beta theta

The association rules that can be determined from this database

1. 100% of sets with alpha also contain beta

we can also illustrate this through a variety of examples.

Assume that a large supermarket tracks sales data by stock-

Let the database of transactions consist of following itemsets:

We will use Apriori to determine the frequent item sets of this

The ﬁrst step of Apriori is to count up the number of occurrences,

All the itemsets of size 1 have a support of at least 3, so they are

The next step is to generate a list of all pairs of the frequent

in the example, there are no frequent triplets. {2,3,4} is below the

We have thus determined the frequent sets of items in the

width (the total number of items) present in the database.

Later algorithms such as Max-Miner[3] try to identify the maximal

Retrieved from "https://en.wikipedia.org/w/index.php?

Last edited 14 days ago by 89.83.24.70

Content is available under CC BY-SA 3.0 unless otherwise noted.

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