L1-NORM HIGHER-ORDER SINGULAR-VALUE DECOMPOSITION

Higher-Order Singular-Value Decomposition (HOSVD) is a standard algorithm for TUCKER decomposition of tensors. Regretfully, TUCKER decomposition has been shown to be sensitive against outliers in the data, due to its L2-norm-based formulation. In this paper, we first introduce L1-TUCKER, an outlier-resistant L1-norm-based variant of TUCKER decomposition. Then, we present L1-HOSVD, a novel algorithm for the solution of L1-TUCKER. Our numerical studies illustrate the outlier resistance of L1-HOSVD compared to HOSVD and other state-of-the-art methods.