{"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/a-nonlinear-orthogonal-non-negative-matrix","title":"A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering","arxiv_id":"1709.10323","date":"2017-09-29","proceeding":null,"authors":["Dijana Tolic","Nino Antulov-Fantulin","Ivica Kopriva"],"abstract":"A recent theoretical analysis shows the equivalence between non-negative\nmatrix factorization (NMF) and spectral clustering based approach to subspace\nclustering. As NMF and many of its variants are essentially linear, we\nintroduce a nonlinear NMF with explicit orthogonality and derive general\nkernel-based orthogonal multiplicative update rules to solve the subspace\nclustering problem. In nonlinear orthogonal NMF framework, we propose two\nsubspace clustering algorithms, named kernel-based non-negative subspace\nclustering KNSC-Ncut and KNSC-Rcut and establish their connection with spectral\nnormalized cut and ratio cut clustering. We further extend the nonlinear\northogonal NMF framework and introduce a graph regularization to obtain a\nfactorization that respects a local geometric structure of the data after the\nnonlinear mapping. The proposed NMF-based approach to subspace clustering takes\ninto account the nonlinear nature of the manifold, as well as its intrinsic\nlocal geometry, which considerably improves the clustering performance when\ncompared to the several recently proposed state-of-the-art methods.","url_abs":"http://arxiv.org/abs/1709.10323v1","url_pdf":"http://arxiv.org/pdf/1709.10323v1.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":"a-nonlinear-orthogonal-non-negative-matrix","repo_url":"https://github.com/singularity4/NonlinearOrthogonalNMF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[{"method_slug":"spectral-clustering","method_name":"Spectral Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1709.10323","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}