{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/decomposition-into-low-rank-plus-additive","title":"Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset","arxiv_id":"1511.01245","date":"2015-11-04","proceeding":null,"authors":["Thierry Bouwmans","Andrews Sobral","Sajid Javed","Soon Ki Jung","El-Hadi Zahzah"],"abstract":"Recent research on problem formulations based on decomposition into low-rank\nplus sparse matrices shows a suitable framework to separate moving objects from\nthe background. The most representative problem formulation is the Robust\nPrincipal Component Analysis (RPCA) solved via Principal Component Pursuit\n(PCP) which decomposes a data matrix in a low-rank matrix and a sparse matrix.\nHowever, similar robust implicit or explicit decompositions can be made in the\nfollowing problem formulations: Robust Non-negative Matrix Factorization\n(RNMF), Robust Matrix Completion (RMC), Robust Subspace Recovery (RSR), Robust\nSubspace Tracking (RST) and Robust Low-Rank Minimization (RLRM). The main goal\nof these similar problem formulations is to obtain explicitly or implicitly a\ndecomposition into low-rank matrix plus additive matrices. In this context,\nthis work aims to initiate a rigorous and comprehensive review of the similar\nproblem formulations in robust subspace learning and tracking based on\ndecomposition into low-rank plus additive matrices for testing and ranking\nexisting algorithms for background/foreground separation. For this, we first\nprovide a preliminary review of the recent developments in the different\nproblem formulations which allows us to define a unified view that we called\nDecomposition into Low-rank plus Additive Matrices (DLAM). Then, we examine\ncarefully each method in each robust subspace learning/tracking frameworks with\ntheir decomposition, their loss functions, their optimization problem and their\nsolvers. Furthermore, we investigate if incremental algorithms and real-time\nimplementations can be achieved for background/foreground separation. Finally,\nexperimental results on a large-scale dataset called Background Models\nChallenge (BMC 2012) show the comparative performance of 32 different robust\nsubspace learning/tracking methods.","url_abs":"http://arxiv.org/abs/1511.01245v3","url_pdf":"http://arxiv.org/pdf/1511.01245v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"decomposition-into-low-rank-plus-additive","repo_url":"https://github.com/andrewssobral/lrslibrary","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}