{"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/optimal-spectral-transportation-with","title":"Optimal spectral transportation with application to music transcription","arxiv_id":"1609.09799","date":"2016-09-30","proceeding":"NeurIPS 2016 12","authors":["Rémi Flamary","Cédric Févotte","Nicolas Courty","Valentin Emiya"],"abstract":"Many spectral unmixing methods rely on the non-negative decomposition of\nspectral data onto a dictionary of spectral templates. In particular,\nstate-of-the-art music transcription systems decompose the spectrogram of the\ninput signal onto a dictionary of representative note spectra. The typical\nmeasures of fit used to quantify the adequacy of the decomposition compare the\ndata and template entries frequency-wise. As such, small displacements of\nenergy from a frequency bin to another as well as variations of timber can\ndisproportionally harm the fit. We address these issues by means of optimal\ntransportation and propose a new measure of fit that treats the frequency\ndistributions of energy holistically as opposed to frequency-wise. Building on\nthe harmonic nature of sound, the new measure is invariant to shifts of energy\nto harmonically-related frequencies, as well as to small and local\ndisplacements of energy. Equipped with this new measure of fit, the dictionary\nof note templates can be considerably simplified to a set of Dirac vectors\nlocated at the target fundamental frequencies (musical pitch values). This in\nturns gives ground to a very fast and simple decomposition algorithm that\nachieves state-of-the-art performance on real musical data.","url_abs":"http://arxiv.org/abs/1609.09799v2","url_pdf":"http://arxiv.org/pdf/1609.09799v2.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":"optimal-spectral-transportation-with","repo_url":"https://github.com/rflamary/OST","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"music-transcription","task_name":"Music Transcription"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1609.09799","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1609.09799"}},"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/rflamary/OST","reach":null}],"summary":{"ran_draft_wrong":3,"ran_fixture":1},"by_repo_kind":{"official":{"samples":4,"ran":4,"repositories":1}},"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":"e5de15a2ddaf4e49","entry":"get_metric","repo":"rflamary/OST","repo_kind":"official","path":"ost.py","file_url":"https://github.com/rflamary/OST/blob/HEAD/ost.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e5de15a2ddaf4e49"}},{"code_sha256_prefix":"ec5d60b1c75a2cfd","entry":"get_pos","repo":"rflamary/OST","repo_kind":"official","path":"demo_unmix.py","file_url":"https://github.com/rflamary/OST/blob/HEAD/demo_unmix.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OPAQUE_PARAMS","metamorphic_tier":"none","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ec5d60b1c75a2cfd"}},{"code_sha256_prefix":"aad5dbbe494624cd","entry":"unmix_fun_fundamental","repo":"rflamary/OST","repo_kind":"official","path":"ost.py","file_url":"https://github.com/rflamary/OST/blob/HEAD/ost.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"aad5dbbe494624cd"}},{"code_sha256_prefix":"0e0f39fe786c882b","entry":"unmix_plan_fundamental","repo":"rflamary/OST","repo_kind":"official","path":"ost.py","file_url":"https://github.com/rflamary/OST/blob/HEAD/ost.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0e0f39fe786c882b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}