Robust Low-rank Tensor Decomposition with the $\operatorname{L_2}$ Criterion

TL;DR

This paper introduces Tucker-L2E, a robust tensor decomposition method based on the L2 criterion, which outperforms existing methods in high-rank scenarios and is validated on various real-world applications.

Contribution

The paper proposes a novel robust Tucker decomposition estimator using the L2 criterion, with data-driven rank selection and demonstrated effectiveness on real data.

Findings

Empirically stronger recovery in high-rank tensor scenarios

Effective data-driven Tucker-rank selection via cross-validation

Successful application in fMRI denoising, fluorescence analysis, and image classification

Abstract

The growing prevalence of tensor data, or multiway arrays, in science and engineering applications motivates the need for tensor decompositions that are robust against outliers. In this paper, we present a robust Tucker decomposition estimator based on the $\operatorname{L_2}$ criterion, called the Tucker-$\operatorname{L_2E}$. Our numerical experiments demonstrate that Tucker-$\operatorname{L_2E}$ has empirically stronger recovery performance in more challenging high-rank scenarios compared with existing alternatives. The appropriate Tucker-rank can be selected in a data-driven manner with cross-validation or hold-out validation. The practical effectiveness of Tucker-$\operatorname{L_2E}$ is validated on real data applications in fMRI tensor denoising, PARAFAC analysis of fluorescence data, and feature extraction for classification of corrupted images.