Mathematics > Numerical Analysis
[Submitted on 19 Mar 2021 (v1), last revised 25 Jun 2021 (this version, v2)]
Title:Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions
View PDFAbstract:Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficient sampling strategy for two primary tensor CUR approximations, namely Chidori and Fiber CUR. We characterize exact tensor CUR decompositions for low multilinear rank tensors. We also present theoretical error bounds of the tensor CUR approximations when (adversarial or Gaussian) noise appears. Moreover, we show that low cost uniform sampling is sufficient for tensor CUR approximations if the tensor has an incoherent structure. Empirical performance evaluations, with both synthetic and real-world datasets, establish the speed advantage of the tensor CUR approximations over other state-of-the-art low multilinear rank tensor approximations.
Submission history
From: Longxiu Huang [view email][v1] Fri, 19 Mar 2021 22:00:21 UTC (29,403 KB)
[v2] Fri, 25 Jun 2021 21:29:00 UTC (2,893 KB)
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