2011/12/16 by Hui Zhang, Jian-Feng Cai, Zhang, Hui +6
Computer Science · Engineering · Mathematics · #Advanced Image Processing Techniques #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Sparse and Compressive Sensing Techniques #cs.IT #cs.LG #math.IT
paper · pdf · doi:10.48550/arxiv.1112.3946
17 pages
openalex publication_date 2011/12/16 · arxiv created 2012/01/05 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently, especially after the publication of the pioneering works of Cand`es et al.. One fundamental result in MC and RPCA is that nuclear norm based convex optimizations lead to the exact low-rank matrix recovery under suitable conditions. In this paper, we extend this result by showing that strongly convex optimizations can guarantee the exact low-rank matrix recovery as well. The result in this paper not only provides sufficient conditions under which the strongly convex models lead to the exact low-rank matrix recovery, but also guides us on how to choose suitable parameters in practical algorithms.