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Abstract

Recent approaches to independent component analysis (ICA) have used
kernel independence measures to obtain very good performance,
particularly where classical methods experience difficulty (for
instance, sources with near-zero kurtosis). We present Fast Kernel ICA
(FastKICA), a novel optimisation technique for one such kernel
independence measure, the Hilbert-Schmidt independence criterion
(HSIC). Our search procedure uses an approximate Newton method on the
special orthogonal group, where we estimate the Hessian locally about
independence. We employ incomplete Cholesky decomposition to
efficiently compute the gradient and approximate Hessian. FastKICA results in more accurate solutions at a given cost
compared with gradient descent, and is relatively insensitive to local minima
when initialised far from independence. These properties allow kernel approaches to be
extended to problems with larger numbers of sources and observations.
Our method is competitive with other modern and classical ICA
approaches in both speed and accuracy.