Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization

Abstract

Principal-Component Analysis (PCA) is a data processing method with numerous applications in signal processing and machine learning. At the same time, standard PCA has been shown to be very sensitive against faulty/outlying data. On the other hand, L1-norm-based PCA (L1-PCA), seeking to maximize the aggregate absolute projections of the processed data, has demonstrated sturdy corruption resistance. At the same time, in our big data era, there is a need for online (stochastic) algorithms for data analysis with limited storage and computation requirements. To this end, in this paper we extend batch L1-PCA and propose a novel algorithm for stochastic PC calculation based on mean absolute projection maximization, with formal convergence guarantees. Our numerical studies demonstrate the convergence and corroborate the corruption resistance of the proposed method.