Tucker-L_2E: Robust Low-rank Tensor Decomposition with the L_2 Criterion
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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 L_2 criterion called the Tucker-L_2E. Our numerical experiments demonstrate that Tucker-L_2E has empirically stronger recovery performance in more challenging high-rank scenarios compared with existing alternatives. We also characterize Tucker-L_2E's insensitivity to rank overestimation and explore approaches for identifying the appropriate Tucker-rank. The practical effectiveness of Tucker-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.
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