An efficient algorithm for L<inf>1</inf>-norm principal component analysis

Abstract

Principal component analysis (PCA) (also called Karhunen - Loeve transform) has been widely used for dimensionality reduction, denoising, feature selection, subspace detection and other purposes. However, traditional PCA minimizes the sum of squared errors and suffers from both outliers and large feature noises. The L 1 -norm based PCA (more precisely L 1,1 norm) is more robust. Yet, the optimization on L 1 -PCA is much harder than standard PCA. In this paper, we propose a simple yet efficient algorithm to solve the L 1 -PCA problem. We carry out extensive experiments to evaluate the proposed algorithm, and verify the robustness against image occlusions. Both numerical and visual results show that L 1 -PCA is consistently better than standard PCA.