An efficient algorithm for L1-norm principal component analysis

Principal component analysis (PCA) (also called Karhunen - Loève 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 L₁-norm based PCA (more precisely L_1,1 norm) is more robust. Yet, the optimization on L₁-PCA is much harder than standard PCA. In this paper, we propose a simple yet efficient algorithm to solve the L₁-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 L₁-PCA is consistently better than standard PCA.