Exact Recovery of Sparsely-Used Dictionaries
Abstract
We consider the problem of learning sparsely used dictionaries with an arbitrary square dictionary and a random, sparse coefficient matrix. We prove that \emphO(n log \emphn) 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.
Cite
Text
Spielman et al. "Exact Recovery of Sparsely-Used Dictionaries." Proceedings of the 25th Annual Conference on Learning Theory, 2012.Markdown
[Spielman et al. "Exact Recovery of Sparsely-Used Dictionaries." Proceedings of the 25th Annual Conference on Learning Theory, 2012.](https://mlanthology.org/colt/2012/spielman2012colt-exact/)BibTeX
@inproceedings{spielman2012colt-exact,
title = {{Exact Recovery of Sparsely-Used Dictionaries}},
author = {Spielman, Daniel A. and Wang, Huan and Wright, John},
booktitle = {Proceedings of the 25th Annual Conference on Learning Theory},
year = {2012},
pages = {37.1-37.18},
volume = {23},
url = {https://mlanthology.org/colt/2012/spielman2012colt-exact/}
}