Exact Recovery of Sparsely-Used Dictionaries
Machine Learning
2012-06-27 v1 Information Theory
math.IT
Abstract
We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that samples are sufficient to uniquely determine the coefficient matrix. Based on this proof, we design a polynomial-time algorithm, called Exact Recovery of Sparsely-Used Dictionaries (ER-SpUD), and prove that it probably recovers the dictionary and coefficient matrix when the coefficient matrix is sufficiently sparse. Simulation results show that ER-SpUD reveals the true dictionary as well as the coefficients with probability higher than many state-of-the-art algorithms.
Keywords
Cite
@article{arxiv.1206.5882,
title = {Exact Recovery of Sparsely-Used Dictionaries},
author = {Daniel A. Spielman and Huan Wang and John Wright},
journal= {arXiv preprint arXiv:1206.5882},
year = {2012}
}