Computational Intractability of Dictionary Learning for Sparse Representation
Machine Learning
2015-11-06 v1 Machine Learning
Abstract
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies, we propose efficient dictionary learning schemes to solve several practical formulations of this problem to stationary points. Unlike many existing algorithms in the literature, such as K-SVD, our proposed dictionary learning scheme is theoretically guaranteed to converge to the set of stationary points under certain mild assumptions. For the image denoising application, the performance and the efficiency of the proposed dictionary learning scheme are comparable to that of K-SVD algorithm in simulation.
Cite
@article{arxiv.1511.01776,
title = {Computational Intractability of Dictionary Learning for Sparse Representation},
author = {Meisam Razaviyayn and Hung-Wei Tseng and Zhi-Quan Luo},
journal= {arXiv preprint arXiv:1511.01776},
year = {2015}
}