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An Expectation-Maximization Approach to Nonlinear Component Analysis

Computational Intelligence Research Unit, Department of Computing and Information Systems, University of Paisley, Paisley, PA1 2BE, Scotland, U.K.

Mark Girolami

Computational Intelligence Research Unit, Department of Computing and Information Systems, University of Paisley, Paisley, PA1 2BE, Scotland, U.K.

The proposal of considering nonlinear principal component analysis as a kernel eigenvalue problem has provided an extremely powerful method of extracting nonlinear features for a number of classification and regression applications. Whereas the utilization of Mercer kernels makes the problem of computing principal components in, possibly, infinite-dimensional feature spaces tractable, there are still the attendant numerical problems of diagonalizing large matrices. In this contribution, we propose an expectation-maximization approach for performing kernel principal component analysis and show this to be a computationally efficient method, especially when the number of data points is large.

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