{"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/automatic-relevance-determination-in","title":"Automatic Relevance Determination in Nonnegative Matrix Factorization with the β-Divergence","arxiv_id":"1111.6085","date":"2011-11-25","proceeding":null,"authors":["Vincent Y. F. Tan","Cédric Févotte"],"abstract":"This paper addresses the estimation of the latent dimensionality in\nnonnegative matrix factorization (NMF) with the \\beta-divergence. The\n\\beta-divergence is a family of cost functions that includes the squared\nEuclidean distance, Kullback-Leibler and Itakura-Saito divergences as special\ncases. Learning the model order is important as it is necessary to strike the\nright balance between data fidelity and overfitting. We propose a Bayesian\nmodel based on automatic relevance determination in which the columns of the\ndictionary matrix and the rows of the activation matrix are tied together\nthrough a common scale parameter in their prior. A family of\nmajorization-minimization algorithms is proposed for maximum a posteriori (MAP)\nestimation. A subset of scale parameters is driven to a small lower bound in\nthe course of inference, with the effect of pruning the corresponding spurious\ncomponents. We demonstrate the efficacy and robustness of our algorithms by\nperforming extensive experiments on synthetic data, the swimmer dataset, a\nmusic decomposition example and a stock price prediction task.","url_abs":"http://arxiv.org/abs/1111.6085v3","url_pdf":"http://arxiv.org/pdf/1111.6085v3.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":"automatic-relevance-determination-in","repo_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"paper_slug":"automatic-relevance-determination-in","repo_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"automatic-relevance-determination-in","repo_url":"https://github.com/getzlab/signatureanalyzer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"stock-price-prediction","task_name":"Stock Price Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1111.6085","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1111.6085"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU","reach":{"status":"ok","spdx":"BSD-3-Clause"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/getzlab/signatureanalyzer","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":17},"by_repo_kind":{"listed":{"samples":17,"ran":0,"repositories":2}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"c38bcacfdb70afa9","entry":"ardnmf","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/bnmf.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/bnmf.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"c38bcacfdb70afa9"}},{"code_sha256_prefix":"bdccf6ee69a8b28c","entry":"beta_div","repo":"broadinstitute/SignatureAnalyzer-GPU","repo_kind":"listed","path":"NMF_functions.py","file_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU/blob/HEAD/NMF_functions.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"bdccf6ee69a8b28c"}},{"code_sha256_prefix":"c1b8e9f28c95ecee","entry":"calculate_objective_function","repo":"broadinstitute/SignatureAnalyzer-GPU","repo_kind":"listed","path":"NMF_functions.py","file_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU/blob/HEAD/NMF_functions.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"c1b8e9f28c95ecee"}},{"code_sha256_prefix":"973c7d382f831049","entry":"consensus_cluster","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/consensus.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/consensus.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"973c7d382f831049"}},{"code_sha256_prefix":"98778cebbecf0b94","entry":"consensus_matrix","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_nmf.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_nmf.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"98778cebbecf0b94"}},{"code_sha256_prefix":"efbc49b22f9de573","entry":"cosine_similarity_plot","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_cosine.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_cosine.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"efbc49b22f9de573"}},{"code_sha256_prefix":"51f57da25bfa56d6","entry":"file_loader","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/utils.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"51f57da25bfa56d6"}},{"code_sha256_prefix":"e644b75169269694","entry":"k_dist","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_nmf.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_nmf.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e644b75169269694"}},{"code_sha256_prefix":"0758b82a3d3f41eb","entry":"l2fc","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/utils.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0758b82a3d3f41eb"}},{"code_sha256_prefix":"3dac6aa2e075082f","entry":"run_method_engine","repo":"broadinstitute/SignatureAnalyzer-GPU","repo_kind":"listed","path":"ARD_NMF.py","file_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU/blob/HEAD/ARD_NMF.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"3dac6aa2e075082f"}},{"code_sha256_prefix":"d7167f8240307350","entry":"signature_barplot","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_muts.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_muts.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d7167f8240307350"}},{"code_sha256_prefix":"f2ae8878f7f9dc6b","entry":"signature_barplot_DBS","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_muts.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_muts.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f2ae8878f7f9dc6b"}},{"code_sha256_prefix":"cffb6cddb2edab2a","entry":"split_negatives","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/utils.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/utils.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"cffb6cddb2edab2a"}},{"code_sha256_prefix":"38091941c5979afa","entry":"stacked_bar","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/plotting/_muts.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/plotting/_muts.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"38091941c5979afa"}},{"code_sha256_prefix":"85b6ed2c04cea782","entry":"supervised_ardnmf","repo":"broadinstitute/getzlab-SignatureAnalyzer","repo_kind":"listed","path":"signatureanalyzer/supervised_bnmf.py","file_url":"https://github.com/broadinstitute/getzlab-SignatureAnalyzer/blob/HEAD/signatureanalyzer/supervised_bnmf.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"85b6ed2c04cea782"}},{"code_sha256_prefix":"5e91034ac2316792","entry":"update_H_poisson_L1","repo":"broadinstitute/SignatureAnalyzer-GPU","repo_kind":"listed","path":"NMF_functions.py","file_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU/blob/HEAD/NMF_functions.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"5e91034ac2316792"}},{"code_sha256_prefix":"31f7195ff693f079","entry":"write_output","repo":"broadinstitute/SignatureAnalyzer-GPU","repo_kind":"listed","path":"SignatureAnalyzer-GPU.py","file_url":"https://github.com/broadinstitute/SignatureAnalyzer-GPU/blob/HEAD/SignatureAnalyzer-GPU.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"31f7195ff693f079"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}