L1-norm Tucker Tensor Decomposition

2019/04/13 by Chachlakis, Dimitris G., Prater-Bennette, Ashley, Markopoulos, Panos P.
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1904.06455

Abstract

Tucker decomposition is a common method for the analysis of multi-way/tensor data. Standard Tucker has been shown to be sensitive against heavy corruptions, due to its L2-norm-based formulation which places squared emphasis to peripheral entries. In this work, we explore L1-Tucker, an L1-norm based reformulation of standard Tucker decomposition. After formulating the problem, we present two algorithms for its solution, namely L1-norm Higher-Order Singular Value Decomposition (L1-HOSVD) and L1-norm Higher-Order Orthogonal Iterations (L1-HOOI). The presented algorithms are accompanied by complexity and convergence analysis. Our numerical studies on tensor reconstruction and classification corroborate that L1-Tucker, implemented by means of the proposed methods, attains similar performance to standard Tucker when the processed data are corruption-free, while it exhibits sturdy resistance against heavily corrupted entries.

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