Fast iterative kernel principal component analysis

Abstract

We develop gain adaptation methods that improve convergence of the kernel Hebbian algorithm (KHA) for iterative kernel PCA (Kim et al., 2005). KHA has a scalar gain parameter which is either held constant or decreased according to a predetermined annealing schedule, leading to slow convergence. We accelerate it by incorporating the reciprocal of the current estimated eigenvalues as part of a gain vector. An additional normalization term then allows us to eliminate a tuning parameter in the annealing schedule. Finally we derive and apply stochastic meta-descent (SMD) gain vector adaptation (Schraudolph, 1999, 2002) in reproducing kernel Hilbert space to further speed up convergence. Experimental results on kernel PCA and spectral clustering of USPS digits, motion capture and image denoising, and image super-resolution tasks confirm that our methods converge substantially faster than conventional KHA. To demonstrate scalability, we perform kernel PCA on the entire MNIST data set.