Efficient Matrix Factorization Via Householder Reflections
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Abstract (arXiv)
Motivated by orthogonal dictionary learning problems, we propose a novel method for matrix factorization, where the data matrix Y is a product of a Householder matrix H and a binary matrix X. First, we show that the exact recovery of the factors H and X from Y is guaranteed with Omega(1) columns in Y . Next, we show approximate recovery (in the l∞ sense) can be done in polynomial time(O(np)) with Omega(log n) columns in Y . We hope the techniques in this work help in developing alternate algorithms for orthogonal dictionary learning.
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References · 10
- 2018Learning graphs from data: A signal representation perspectivecited by 119
- 2015Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picturecited by 49
- 2015Simple, Efficient, and Neural Algorithms for Sparse Codingcited by 37
- 2013Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimizationcited by 24
- 2013New Algorithms for Learning Incoherent and Overcomplete Dictionariescited by 22
- 2015Complete Dictionary Recovery over the Spherecited by 19
- 2014Learning parametric dictionaries for graph signalscited by 12
- 2014Local Identification of Overcomplete Dictionariescited by 7
- 2022Simple Alternating Minimization Provably Solves Complete Dictionary Learningcited by 6
- 2017Provable Alternating Gradient Descent for Non-negative Matrix Factorization with Strong Correlationscited by 3
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