Efficient Matrix Factorization Via Householder Reflections

• URL: http://arxiv.org/abs/2405.07649v2
• Date: Fri, 04 Oct 2024 07:42:20 GMT
• Title: Efficient Matrix Factorization Via Householder Reflections
• Authors: Anirudh Dash, Aditya Siripuram,
• Abstract summary: We show that the exact recovery of the factors $mathbfH$ and $mathbfX$ from $mathbfY$ is guaranteed with $Omega$ columns in $mathbfY$. We hope the techniques in this work help in developing alternate algorithms for dictionary learning.
• Score: 2.3326951882644553
• License:
• 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 $\mathbf{Y}$ . We hope the techniques in this work help in developing alternate algorithms for orthogonal dictionary learning.

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