Spectral clustering on manifolds with statistical and geometrical similarity

Authors:
Yong Cheng;Qiang Tong
Affiliations:
Department of Computer Sciences, Beijing University of Chemical Technology;School of Information Technology, University of International Business and Economics
Venue:
ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Year:
2010

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Abstract

The problem of clustering data has been driven by a demand from various disciplines engaged in exploratory data analysis, such as medicine taxonomy, customer relationship management and so on However, Most of the algorithms designed to handle data in the form of point clouds fail to cluster data that expose a manifold structure The high dimensional data sets often exhibit geometrical structures which are often important in clustering data on manifold Motivated by the fact, we believe that a good similarity measure on a manifold should reflect not only the statistical properties but also the geometrical properties of given data We model the similarity between data points in statistical and geometrical perspectives, then a modified version of spectral algorithm on manifold is proposed to reveal the structure The encouraging results on several artificial and real-world data set are obtained which validate our proposed clustering algorithm.