Divide-and-Conquer Computational Approach to Principal Component Analysis

Abstract

Divide-and-Conquer (DC) paradigm is one of the classical approaches for designing algorithms. Principal Component Analysis (PCA) is a widely used technique for dimensionality reduction. The existing block based PCA methods do not fully comply with a formal DC approach because (i) they may discard some of the features, due to partitioning, which may affect recognition; (ii) they do not use recursive algorithm, which is used by DC methods in general to provide natural and elegant solutions. In this paper, we apply DC approach to design a novel algorithm that computes principal components more efficiently and with dimensionality reduction competitive to PCA. Our empirical results on palmprint and face datasets demonstrate the superiority of the proposed approach in terms of recognition and computational complexity as compared to classical PCA and block-based SubXPCA methods. We also demonstrate the improved gross performance of the proposed approach over the block-based SubPCA in terms of dimensionality reduction, computational time, and recognition.