Optimizing the cauchy-schwarz PDF distance for information theoretic, non-parametric clustering

Authors:
Robert Jenssen;Deniz Erdogmus;Kenneth E. Hild;Jose C. Principe;Torbjørn Eltoft
Affiliations:
Department of Physics, University of Tromsø, Tromsø, Norway;Department of Computer Science and Engineering, Oregon Graduate Institute, OHSU, Portland, OR.;Department of Radiology, University of California, San Francisco, CA.;Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL.;Department of Physics, University of Tromsø, Tromsø, Norway
Venue:
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Year:
2005

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Abstract

This paper addresses the problem of efficient information theoretic, non-parametric data clustering. We develop a procedure for adapting the cluster memberships of the data patterns, in order to maximize the recent Cauchy-Schwarz (CS) probability density function (pdf) distance measure. Each pdf corresponds to a cluster. The CS distance is estimated analytically and non-parametrically by means of the Parzen window technique for density estimation. The resulting form of the cost function makes it possible to develop an efficient adaption procedure based on constrained gradient descent, using stochastic approximation of the gradients. The computational complexity of the algorithm is O(MN), M ≪ N, where N is the total number of data patterns and M is the number of data patterns used in the stochastic approximation. We show that the new algorithm is capable of performing well on several odd-shaped and irregular data sets.