{"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/denise-deep-learning-based-robust-pca-for","title":"Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices","arxiv_id":"2004.13612","date":"2020-04-28","proceeding":null,"authors":["Calypso Herrera","Florian Krach","Anastasis Kratsios","Pierre Ruyssen","Josef Teichmann"],"abstract":"The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms must re-run for every new matrix. Since these algorithms are computationally expensive, it is preferable to learn and store a function that nearly instantaneously performs this decomposition when evaluated. Therefore, we introduce Denise, a deep learning-based algorithm for robust PCA of covariance matrices, or more generally, of symmetric positive semidefinite matrices, which learns precisely such a function. Theoretical guarantees for Denise are provided. These include a novel universal approximation theorem adapted to our geometric deep learning problem and convergence to an optimal solution to the learning problem. Our experiments show that Denise matches state-of-the-art performance in terms of decomposition quality, while being approximately $2000\\times$ faster than the state-of-the-art, principal component pursuit (PCP), and $200 \\times$ faster than the current speed-optimized method, fast PCP.","url_abs":"https://arxiv.org/abs/2004.13612v4","url_pdf":"https://arxiv.org/pdf/2004.13612v4.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":"denise-deep-learning-based-robust-pca-for","repo_url":"https://github.com/DeepRPCA/Denise","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"}],"methods":[{"method_slug":"pca","method_name":"PCA"},{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2004.13612","atlas_url":"https://app.syntology.ai/?focus=2004.13612","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}