Accelerated kernel feature analysis

Abstract

A fast algorithm, Accelerated Kernel Feature Analysis (AKFA), that discovers salient features evidenced in a sample of n unclassified patterns, is presented. Like earlier kernel-based feature selection algorithms, AKFA implicitly embeds each pattern into a Hubert space, H, induced by a Mercer kernel. An ℓ-dimensional linear subspace of H is iteratively constructed by maximizing a variance condition for the nonlinearly transformed sample. This linear subspace can then be used to define more efficient data representations and pattern classifiers. AKFA requires O(ℓ/n 2) operations, as compared to O(n 3) for Schölkof, Smola, and Müller's Kernel Principal Component Analysis (KPCA), and O(ℓ 2n 2) for Smola, Mangasarian, and Schölkopf's Sparse Kernel Feature Analysis (SKFA). Numerical experiments show that AKFA can generate more concise feature representations than both KPCA and SKFA, and demonstrate that AKFA obtains similar classification performance as KPCA for a face recognition problem. © 2006 IEEE.