{"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/structured-sparse-non-negative-matrix","title":"Structured Sparse Non-negative Matrix Factorization with L20-Norm for scRNA-seq Data Analysis","arxiv_id":"2104.13171","date":"2021-04-27","proceeding":null,"authors":["Wenwen Min","Taosheng Xu","Xiang Wan","Tsung-Hui Chang"],"abstract":"Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data without effective feature selection. In this paper, we first introduce a row-sparse NMF with $\\ell_{2,0}$-norm constraint (NMF_$\\ell_{20}$), where the basis matrix $W$ is constrained by the $\\ell_{2,0}$-norm, such that $W$ has a row-sparsity pattern with feature selection. It is a challenge to solve the model, because the $\\ell_{2,0}$-norm is non-convex and non-smooth. Fortunately, we prove that the $\\ell_{2,0}$-norm satisfies the Kurdyka-\\L{ojasiewicz} property. Based on the finding, we present a proximal alternating linearized minimization algorithm and its monotone accelerated version to solve the NMF_$\\ell_{20}$ model. In addition, we also present a orthogonal NMF with $\\ell_{2,0}$-norm constraint (ONMF_$\\ell_{20}$) to enhance the clustering performance by using a non-negative orthogonal constraint. We propose an efficient algorithm to solve ONMF_$\\ell_{20}$ by transforming it into a series of constrained and penalized matrix factorization problems. The results on numerical and scRNA-seq datasets demonstrate the efficiency of our methods in comparison with existing methods.","url_abs":"https://arxiv.org/abs/2104.13171v1","url_pdf":"https://arxiv.org/pdf/2104.13171v1.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":"structured-sparse-non-negative-matrix","repo_url":"https://github.com/wenwenmin/SSNMF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}