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Abstract

Recent approaches to independent component analysis have used kernel
independence measures to obtain very good performance in ICA, particularly
in areas where classical methods experience difficulty (for instance,
sources with near-zero kurtosis). In this chapter, we compare two efficient
extensions of these methods for large-scale problems: random subsampling
of entries in the Gram matrices used in defining the independence
measures, and incomplete Cholesky decomposition of these matrices.
We derive closed-form, efficiently computable approximations for the
gradients of these measures, and compare their performance on ICA using
both artificial and music data. We show that kernel ICA can scale up to much larger
problems than yet attempted, and that incomplete Cholesky decomposition
performs better than random sampling.