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.
This work was partially supported by NSF grants ECS-9900394 and EIA-0135946.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jain, A.K., Murty, M.N., Flynn, P.J.: Data Clustering: A Review. ACM Computing Surveys 31(3), 264–323 (1999)
Bezdek, J.C.: A Convergence Theorem for the Fuzzy Isodata Clustering Algorithms. IEEE Transactions on Pattern Analysis and Machine Learning 2(1), 1–8 (1980)
McLachlan, G.J., Peel, D.: Finite Mixture Models. John Wiley & Sons, New York (2000)
Rose, K., Gurewitz, E., Fox, G.C.: Vector Quantization by Deterministic Annealing. IEEE Transactions on Information Theory 38(4), 1249–1257 (1992)
Hofmann, T., Buhmann, J.M.: Pairwise Data Clustering by Deterministic Annealing. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(1), 1–14 (1997)
Roberts, S.J., Everson, R., Rezek, I.: Maximum Certainty Data Partitioning. Pattern Recognition 33, 833–839 (2000)
Tishby, N., Slonim, N.: Data Clustering by Markovian Relaxation and the Information Bottleneck Method. In: Advances in Neural Information Processing Systems, vol. 13, pp. 640–646. MIT Press, Cambridge (2001)
Principe, J., Xu, D., Fisher, J.: Information Theoretic Learning. In: Haykin, S. (ed.) Unsupervised Adaptive Filtering, ch. 7, vol. I. John Wiley & Sons, New York (2000)
Parzen, E.: On the Estimation of a Probability Density Function and the Mode. The Annals of Mathematical Statistics 32, 1065–1076 (1962)
Gokcay, E., Principe, J.: Information Theoretic Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(2), 158–170 (2002)
Milligan, G.W., Cooper, M.C.: An Examination of Procedures for Determining the Number of Clusters in a Data Set. Phychometrica, 159–179 (1985)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986)
Shi, J., Malik, J.: Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Mangasarian, O.L., Wolberg, W.H.: Cancer Diagnosis via Linear Programming. SIAM News 5, 1–18 (1990)
Jenssen, R., Principe, J.C., Eltoft, T.: Information Cut and Information Forces for Clustering. In: Proceedings of IEEE International Workshop on Neural Networks for Signal Processing, Toulouse, France, September 17-19, pp. 459–468 (2003)
Jenssen, R., Erdogmus, D., Principe, J.C., Eltoft, T.: The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space. In: Advances in Neural Information Processing Systems, vol. 17, pp. 625–632. MIT Press, Cambridge (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jenssen, R., Erdogmus, D., Hild, K.E., Principe, J.C., Eltoft, T. (2005). Optimizing the Cauchy-Schwarz PDF Distance for Information Theoretic, Non-parametric Clustering. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_3
Download citation
DOI: https://doi.org/10.1007/11585978_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30287-2
Online ISBN: 978-3-540-32098-2
eBook Packages: Computer ScienceComputer Science (R0)