K-medians clustering based ℓ1-PCA model

Shu Yan Lam, Siu-Kai Choy

Abstract: Principal Component Analysis (PCA) is one of the most widely used tools for the representation of high-dimensional data. Many different versions have been proposed to enhance the robustness of the model. Most of these ideas are not median based formulation, which is always a robust estimator in statistics. In this paper, we attempt to design a new median based PCA model based on k-medians clustering, for which each principal component is always the spatial median of the projected space. We prove that the proposed method converges. We also compare the proposed method with several state-of-the-art methods including ℓ1-PCA, RPCA and RPCA-OM. Experimental results show that the proposed k-medians clustering based PCA performs the best in many cases.