English

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 global\textit{global} 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.

Keywords

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

R2 v1 2026-06-23T07:47:26.996Z