Papers › Robust Low-rank Tensor Decomposition with the L₂ Criterion
Robust Low-rank Tensor Decomposition with the L₂ Criterion
Qiang Heng, Eric C. Chi, Yufeng Liu
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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 L₂ criterion, called the Tucker-L₂E. Our numerical experiments demonstrate that Tucker-L₂E 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-L₂E 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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