Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization PrincipalComponent 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 faultyoutlying data. On the other hand, L1normbased PCA (L1PCA), 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 L1PCA 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.

Robust MultiRelational Learning With Absolute Projection Rescal RESCAL is a popular approach for multirelational learning based on tensor decomposition. At the same time, RESCAL follows a L2norm formulation that can be very sensitive against outlying data corruptions. In this work, we propose ARESCAL: a corruptionresistant reformulation of RESCAL based on absolute projections. Specifically, we (i) show that rank1 ARESCAL can be cast as a combinatorial problem over antipodal binary variables and solve it exactly by exhaustive search; (ii) develop an efficient iterative algorithm for approximating the solution to rank1 ARESCAL; and (iii) extend our solver for general rank by means of subspace deflation. Our experimental studies on multiple benchmark datasets show that ARESCAL performs quite similarly to standard RESCAL when the processed data are nominal, while it is significantly more robust in the case of data corruption.