Article

Dimension induced clustering

Authors:

Aristides Gionis,

Alexander Hinneburg,

Spiros Papadimitriou,

Panayiotis TsaparasAuthors Info & Claims

KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining

Pages 51 - 60

https://doi.org/10.1145/1081870.1081880

Published: 21 August 2005 Publication History

Abstract

It is commonly assumed that high-dimensional datasets contain points most of which are located in low-dimensional manifolds. Detection of low-dimensional clusters is an extremely useful task for performing operations such as clustering and classification, however, it is a challenging computational problem. In this paper we study the problem of finding subsets of points with low intrinsic dimensionality. Our main contribution is to extend the definition of fractal correlation dimension, which measures average volume growth rate, in order to estimate the intrinsic dimensionality of the data in local neighborhoods. We provide a careful analysis of several key examples in order to demonstrate the properties of our measure. Based on our proposed measure, we introduce a novel approach to discover clusters with low dimensionality. The resulting algorithms extend previous density based measures, which have been successfully used for clustering. We demonstrate the effectiveness of our algorithms for discovering low-dimensional m-flats embedded in high dimensional spaces, and for detecting low-rank sub-matrices.

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Cited By

Gevorgyan RHakobyan Y(2023)Perspective Chapter: Matching-Based Clustering Algorithm for Categorical DataBlockchain Applications - Transforming Industries, Enhancing Security, and Addressing Ethical Considerations10.5772/intechopen.109548Online publication date: 26-Jul-2023
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Houle MKiermeier MZimek A(2023)Clustering High-Dimensional DataMachine Learning for Data Science Handbook10.1007/978-3-031-24628-9_11(219-237)Online publication date: 26-Feb-2023
https://doi.org/10.1007/978-3-031-24628-9_11
Bac JMirkes EGorban ATyukin IZinovyev A(2021)Scikit-Dimension: A Python Package for Intrinsic Dimension EstimationEntropy10.3390/e2310136823:10(1368)Online publication date: 19-Oct-2021
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Index Terms

Dimension induced clustering
1. Information systems

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Published In

cover image ACM Conferences

KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining

August 2005

844 pages

ISBN:159593135X

DOI:10.1145/1081870

General Chair:
Robert Grossman
University of Illinois at Chicago & Open Data Partners, USA
,
Program Chairs:
Roberto Bayardo
IBM Almaden Research, USA
,
Kristin Bennett
RPI, USA

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 21 August 2005

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KDD05: The Eleventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

August 21 - 24, 2005

Illinois, Chicago, USA

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Overall Acceptance Rate 1,133 of 8,635 submissions, 13%

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Cited By

Gevorgyan RHakobyan Y(2023)Perspective Chapter: Matching-Based Clustering Algorithm for Categorical DataBlockchain Applications - Transforming Industries, Enhancing Security, and Addressing Ethical Considerations10.5772/intechopen.109548Online publication date: 26-Jul-2023
https://doi.org/10.5772/intechopen.109548
Houle MKiermeier MZimek A(2023)Clustering High-Dimensional DataMachine Learning for Data Science Handbook10.1007/978-3-031-24628-9_11(219-237)Online publication date: 26-Feb-2023
https://doi.org/10.1007/978-3-031-24628-9_11
Bac JMirkes EGorban ATyukin IZinovyev A(2021)Scikit-Dimension: A Python Package for Intrinsic Dimension EstimationEntropy10.3390/e2310136823:10(1368)Online publication date: 19-Oct-2021
https://doi.org/10.3390/e23101368
Kanevski M(2021)Unsupervised learning of Swiss population spatial distributionPLOS ONE10.1371/journal.pone.024652916:2(e0246529)Online publication date: 11-Feb-2021
https://doi.org/10.1371/journal.pone.0246529
Xu DYang HGu CChen ZXuan QYang X(2021)Adversarial Examples Detection of Radio Signals Based on Multifeature FusionIEEE Transactions on Circuits and Systems II: Express Briefs10.1109/TCSII.2021.309566368:12(3607-3611)Online publication date: Dec-2021
https://doi.org/10.1109/TCSII.2021.3095663
Kanevski MLaib M(2021)Unsupervised Learning of High Dimensional Environmental Data Using Local Fractality ConceptPattern Recognition. ICPR International Workshops and Challenges10.1007/978-3-030-68780-9_13(130-138)Online publication date: 25-Feb-2021
https://doi.org/10.1007/978-3-030-68780-9_13
Allegra MFacco EDenti FLaio AMira A(2020)Data segmentation based on the local intrinsic dimensionScientific Reports10.1038/s41598-020-72222-010:1Online publication date: 5-Oct-2020
https://doi.org/10.1038/s41598-020-72222-0
Yang JZhai GDuan H(2019)Predicting the visual saliency of the people with VIMS2019 IEEE Visual Communications and Image Processing (VCIP)10.1109/VCIP47243.2019.8965925(1-4)Online publication date: Dec-2019
https://doi.org/10.1109/VCIP47243.2019.8965925
Yang TLi C(2019)Local Convex Representation with Pruning for Manifold Clustering2019 IEEE Visual Communications and Image Processing (VCIP)10.1109/VCIP47243.2019.8965757(1-4)Online publication date: Dec-2019
https://doi.org/10.1109/VCIP47243.2019.8965757
Zhang ZLiu NFeng XWang DYang LWang Z(2019)Shape Representation of Fractal Dimension on Point Cloud2019 Nicograph International (NicoInt)10.1109/NICOInt.2019.00027(102-105)Online publication date: Jul-2019
https://doi.org/10.1109/NICOInt.2019.00027
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