Sparse PCA: Extracting Multi-Scale Structure from Data

Abstract

Sparse Principal Component Analysis (S-PCA) is a novel framework for learning a linear, orthonormal basis representation for structure intrinsic to an ensemble of images. S-PCA is based on the discovery that natural images exhibit structure in a low-dimensional subspace in a sparse, scale-dependent form. The S-PCA basis optimizes an objective function which trades off correlations among output coefficients for sparsity in the description of basis vector elements. This objective function is minimized by a simple, robust and highly scalable adaptation algorithm, consisting of successive planar rotations of pairs of basis vectors. The formulation of S-PCA is novel in that multi-scale representations emerge for a variety of ensembles including face images, images from outdoor scenes and a database of optical flow vectors representing a motion class.