Robust Barron-Loss Tucker Tensor Decomposition

Abstract

Tucker decomposition is a standard method for the analysis of high-order tensor data. Standard Tucker decomposition generalizes singular-value decomposition and is formulated as minimization of the L2-norm of the low-rank approximation error. Due to the quadratic emphasis on peripheral data, the L2-norm based formulation of Tucker has been shown to be sensitive against corruptions. L1-norm-based variants (L1-Tucker) are proposed as robust Tucker decomposition methods, and are formulated as subspace estimators by absolute-projection maximization, and have proven effective in outlier resistant subspace computation. However, Tucker decomposition for robust low-rank tensor approximation is not defined/optimized in the literature. In this work, we propose a new formulation for low-rank tensor approximation, with tunable outlier-robustness, and present a unified algorithmic solution framework. This formulation relies on a new generalized robust loss function (Barron loss), which encompasses several well-known loss-functions with variable outlier-resistance. The robustness of the proposed framework is corroborated by the presented numerical studies on synthetic and real data.