Kernel Independent Component Analysis

Francis R. Bach
(Professor Michael I. Jordan)
Intel Corporation, (NSF) IIS-9988642, and (ONR/MURI) N00014-00-1-0637

Independent component analysis is a recent statistical method for revealing hidden factors of sets of random variables, where the hidden factors (the components) are assumed to be statistically independent. It has been successfully applied to problems such as audio blind source separation--the so-called "cocktail party" problem, where streams of overlapping speech have to be separated according to the individual speakers--and biomedical data processing.

Kernel methods, as exemplified by support vector machines, are a novel paradigm for pattern recognition. They efficiently enable one to extend well-known and well-studied linear techniques to become nonlinear techniques.

The object of our work is to use kernel methods to perform ICA. We show how, by applying the classical multivariate statistical technique of canonical correlations to a kernel space, we obtain a family of nonlinear ICA algorithms. On synthetic examples, our "Kernel-ICA" algorithms outperform many of the known algorithms for ICA.

F. R. Bach and M. I. Jordan, "Kernel Independent Component Analysis," J. Machine Learning Research, Vol. 3, 2002.
A. Hyvarinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, 2001.
B. Scholkopf and A. J. Smola, Learning with Kernels, MIT Press, 2001.

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