Cauchy Principal Component Analysis

Abstract

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Principal Component Analysis (Cauchy PCA), a very simple yet effective PCA method which is robust to various types of noise. We utilize Cauchy distribution to model noise and derive Cauchy PCA under the maximum likelihood estimation (MLE) framework with low rank constraint. Our method can robustly estimate the low rank matrix regardless of whether noise is large or small, dense or sparse. We analyze the robustness of Cauchy PCA from a robust statistics view and present an efficient singular value projection optimization method. Experimental results on both simulated data and real applications demonstrate the robustness of Cauchy PCA to various noise patterns.