L1-Norm Higher-Order Orthogonal Iterations for Robust Tensor Analysis

Dimitris G. Chachlakis, Ashley Prater-Bennette, Panos P. Markopoulos

Abstract: Standard Tucker tensor decomposition seeks to maximize the L2-norm of the compressed tensor; thus, it is very responsive to outlying/high-magnitude entries among the processed data. To counteract the impact of outliers in tensor data analysis, we propose L1-Tucker: a reformulation of standard Tucker decomposition, resulting by simple substitution of the outlier-responsive L2-norm by the sturdier L1-norm. Then, we propose the L1-norm Higher Order Orthogonal Iterations (L1-HOOI) algorithm for the approximate solution to L1-Tucker. Our numerical studies on data reconstruction and classification corroborate that L1-HOOI exhibits sturdy resistance against outliers compared to standard counterparts.