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Mode-wise Tensor Decompositions: Multi-dimensional Generalizations of CUR Decompositions
HanQin Cai, Keaton Hamm, Longxiu Huang +1
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 efficie…
Stability of Sampling for CUR Decompositions
Keaton Hamm, Longxiu Huang
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well.…
Perturbations of CUR Decompositions
Keaton Hamm, Longxiu Huang
The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to…
Perspectives on CUR Decompositions
Keaton Hamm, Longxiu Huang
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different…