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DOE OSTI · 2430043

The Average Spectrum Norm and Near-Optimal Tensor Completion

Lopez, Oscar F.·Lehoucq, Richard B.·Llosa, Carlos·Prasadan, Arvind·Dunlavy, Daniel Michael
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Abstract

We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.

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97 MATHEMATICS AND COMPUTINGcanonical polyadic tensor decompositiondual normspectral normtensor completion

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BibTeXRIS

Lopez, Oscar F., Lehoucq, Richard B., Llosa, Carlos, Prasadan, Arvind, Dunlavy, Daniel Michael. 2024-08-17. The Average Spectrum Norm and Near-Optimal Tensor Completion. https://doi.org/10.2172/2430043

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