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Efficient Matrix Factorization Via Householder Reflections
May 14, 2024, 4:43 a.m. | Anirudh Dash, Aditya Siripuram
cs.LG updates on arXiv.org arxiv.org
Abstract: Motivated by orthogonal dictionary learning problems, we propose a novel method for matrix factorization, where the data matrix $\mathbf{Y}$ is a product of a Householder matrix $\mathbf{H}$ and a binary matrix $\mathbf{X}$. First, we show that the exact recovery of the factors $\mathbf{H}$ and $\mathbf{X}$ from $\mathbf{Y}$ is guaranteed with $\Omega(1)$ columns in $\mathbf{Y}$ . Next, we show approximate recovery (in the $l\infty$ sense) can be done in polynomial time($O(np)$) with $\Omega(\log n)$ columns in …
abstract arxiv binary cs.lg data dictionary eess.sp factorization matrix novel product recovery reflections show type via
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