Year: 2023
Author: Guang-Jing Song, Michael K. Ng
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 181–205
Abstract
In this paper, we study Riemannian optimization methods for the problem of nonnegative matrix completion that is to recover a nonnegative low rank matrix from its partial observed entries. With the underlying matrix incoherence conditions, we show that when the number $m$ of observed entries are sampled independently and uniformly without replacement, the inexact Riemannian gradient descent method can recover the underlying $n_{1}$-by-$n_{2}$ nonnegative matrix of rank $r$ provided that $m$ is of $\mathcal{O}(r^{2} s \log^2s )$, where $s = \max \{n_{1},n_{2} \}$. Numerical examples are given to illustrate that the nonnegativity property would be useful in the matrix recovery. In particular, we demonstrate the number of samples required to recover the underlying low rank matrix with using the nonnegativity property is smaller than that without using the property.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2023-0010
Annals of Applied Mathematics, Vol. 39 (2023), Iss. 2 : pp. 181–205
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Manifolds tangent spaces nonnegative matrices low rank.