A Dictionary Based Generalization of Robust PCA
Machine Learning
2019-02-22 v1 Optimization and Control
Machine Learning
Abstract
We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both undercomplete and overcomplete dictionary cases, and show that the constituent components can be successfully recovered under some relatively mild assumptions up to a certain sparsity level. Further, we corroborate our theoretical results by presenting empirical evaluations in terms of phase transitions in rank and sparsity for various dictionary sizes.
Cite
@article{arxiv.1902.08171,
title = {A Dictionary Based Generalization of Robust PCA},
author = {Sirisha Rambhatla and Xingguo Li and Jarvis Haupt},
journal= {arXiv preprint arXiv:1902.08171},
year = {2019}
}
Comments
5 pages; Index terms -- Low-rank, Dictionary sparse, Matrix Demixing, and Generalized Robust PCA