IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Direct Approximation of Quadratic Mutual Information and Its Application to Dependence-Maximization Clustering
Janya SAINUIMasashi SUGIYAMA
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2013 Volume E96.D Issue 10 Pages 2282-2285

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Abstract

Mutual information (MI) is a standard measure of statistical dependence of random variables. However, due to the log function and the ratio of probability densities included in MI, it is sensitive to outliers. On the other hand, the L2-distance variant of MI called quadratic MI (QMI) tends to be robust against outliers because QMI is just the integral of the squared difference between the joint density and the product of marginals. In this paper, we propose a kernel least-squares QMI estimator called least-squares QMI (LSQMI) that directly estimates the density difference without estimating each density. A notable advantage of LSQMI is that its solution can be analytically and efficiently computed just by solving a system of linear equations. We then apply LSQMI to dependence-maximization clustering, and demonstrate its usefulness experimentally.

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© 2013 The Institute of Electronics, Information and Communication Engineers
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