{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TMWOLAMKFXBVKLPJPFG6AUKC2W","short_pith_number":"pith:TMWOLAMK","canonical_record":{"source":{"id":"2110.14434","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SD","submitted_at":"2021-10-27T13:46:51Z","cross_cats_sorted":["cs.LG","cs.NA","eess.AS","math.NA"],"title_canon_sha256":"7d30705fafc8a377aeb27d3b8bbee010dc831814c57a89d7063f980bfb60e5d1","abstract_canon_sha256":"4ac8729f62a1d03d03e4e50f07e06616d21d32eeb65157b7e59ec9b000dcb538"},"schema_version":"1.0"},"canonical_sha256":"9b2ce5818a2dc3552de9794de05142d5b81c286ba78f9a21d49a004cafb466b5","source":{"kind":"arxiv","id":"2110.14434","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14434","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14434v4","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14434","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"TMWOLAMKFXBV","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_16","alias_value":"TMWOLAMKFXBVKLPJ","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_8","alias_value":"TMWOLAMK","created_at":"2026-07-05T04:45:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TMWOLAMKFXBVKLPJPFG6AUKC2W","target":"record","payload":{"canonical_record":{"source":{"id":"2110.14434","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SD","submitted_at":"2021-10-27T13:46:51Z","cross_cats_sorted":["cs.LG","cs.NA","eess.AS","math.NA"],"title_canon_sha256":"7d30705fafc8a377aeb27d3b8bbee010dc831814c57a89d7063f980bfb60e5d1","abstract_canon_sha256":"4ac8729f62a1d03d03e4e50f07e06616d21d32eeb65157b7e59ec9b000dcb538"},"schema_version":"1.0"},"canonical_sha256":"9b2ce5818a2dc3552de9794de05142d5b81c286ba78f9a21d49a004cafb466b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:12.595136Z","signature_b64":"AkCcae1Anu/un2P6VnRL0zk5auMF5wPDm6Q/Mzehfj8iWGyOp2e7qzdNc66hOd5WsJrbxBZysS+oy9W4U3VyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b2ce5818a2dc3552de9794de05142d5b81c286ba78f9a21d49a004cafb466b5","last_reissued_at":"2026-07-05T04:45:12.594649Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:12.594649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.14434","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRbwgTKm5VH7t851ngYtEDpX6277TjDTHanvo2syJWB9MSHQ3m9vGwio2E4vM9Mn+jJqZppHmorkaiBwBrX1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:04:45.684266Z"},"content_sha256":"3476e6f8f220f58db33cb828ac4e2c4a6f1943a00235d880ecdaed276932d181","schema_version":"1.0","event_id":"sha256:3476e6f8f220f58db33cb828ac4e2c4a6f1943a00235d880ecdaed276932d181"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TMWOLAMKFXBVKLPJPFG6AUKC2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","eess.AS","math.NA"],"primary_cat":"cs.SD","authors_text":"Axel Marmoret, Florian Voorwinden, Fr\\'ed\\'eric Bimbot, J\\'er\\'emy E. Cohen, Valentin Leplat","submitted_at":"2021-10-27T13:46:51Z","abstract_excerpt":"Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval. Nevertheless, existing algorithms to compute NTD are mostly designed for the Euclidean loss. This work proposes a multiplicative updates algorithm to compute NTD with the beta-divergence loss, often considered a better loss for audio processing. We notably show how to implement efficiently the multiplicative rules using tensor algebra. Finally, we show on a music str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14434","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14434/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"an5lSuoX1fE4MILDfpxTHJLcPXZRcldVUgy7o4IXMMLf8KEJktpZURa9nlFvmMi/hHlhQjg4eIH0JBV5vmBNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:04:45.684671Z"},"content_sha256":"b7b2c6e59c00e1c56624a42d476baeb419d83074bade4e94c3bdec7321cba792","schema_version":"1.0","event_id":"sha256:b7b2c6e59c00e1c56624a42d476baeb419d83074bade4e94c3bdec7321cba792"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/bundle.json","state_url":"https://pith.science/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-05T09:04:45Z","links":{"resolver":"https://pith.science/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W","bundle":"https://pith.science/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/bundle.json","state":"https://pith.science/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMWOLAMKFXBVKLPJPFG6AUKC2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TMWOLAMKFXBVKLPJPFG6AUKC2W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4ac8729f62a1d03d03e4e50f07e06616d21d32eeb65157b7e59ec9b000dcb538","cross_cats_sorted":["cs.LG","cs.NA","eess.AS","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SD","submitted_at":"2021-10-27T13:46:51Z","title_canon_sha256":"7d30705fafc8a377aeb27d3b8bbee010dc831814c57a89d7063f980bfb60e5d1"},"schema_version":"1.0","source":{"id":"2110.14434","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14434","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14434v4","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14434","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"TMWOLAMKFXBV","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_16","alias_value":"TMWOLAMKFXBVKLPJ","created_at":"2026-07-05T04:45:12Z"},{"alias_kind":"pith_short_8","alias_value":"TMWOLAMK","created_at":"2026-07-05T04:45:12Z"}],"graph_snapshots":[{"event_id":"sha256:b7b2c6e59c00e1c56624a42d476baeb419d83074bade4e94c3bdec7321cba792","target":"graph","created_at":"2026-07-05T04:45:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.14434/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information Retrieval. Nevertheless, existing algorithms to compute NTD are mostly designed for the Euclidean loss. This work proposes a multiplicative updates algorithm to compute NTD with the beta-divergence loss, often considered a better loss for audio processing. We notably show how to implement efficiently the multiplicative rules using tensor algebra. Finally, we show on a music str","authors_text":"Axel Marmoret, Florian Voorwinden, Fr\\'ed\\'eric Bimbot, J\\'er\\'emy E. Cohen, Valentin Leplat","cross_cats":["cs.LG","cs.NA","eess.AS","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SD","submitted_at":"2021-10-27T13:46:51Z","title":"Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14434","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3476e6f8f220f58db33cb828ac4e2c4a6f1943a00235d880ecdaed276932d181","target":"record","created_at":"2026-07-05T04:45:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4ac8729f62a1d03d03e4e50f07e06616d21d32eeb65157b7e59ec9b000dcb538","cross_cats_sorted":["cs.LG","cs.NA","eess.AS","math.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SD","submitted_at":"2021-10-27T13:46:51Z","title_canon_sha256":"7d30705fafc8a377aeb27d3b8bbee010dc831814c57a89d7063f980bfb60e5d1"},"schema_version":"1.0","source":{"id":"2110.14434","kind":"arxiv","version":4}},"canonical_sha256":"9b2ce5818a2dc3552de9794de05142d5b81c286ba78f9a21d49a004cafb466b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b2ce5818a2dc3552de9794de05142d5b81c286ba78f9a21d49a004cafb466b5","first_computed_at":"2026-07-05T04:45:12.594649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:45:12.594649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AkCcae1Anu/un2P6VnRL0zk5auMF5wPDm6Q/Mzehfj8iWGyOp2e7qzdNc66hOd5WsJrbxBZysS+oy9W4U3VyBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:45:12.595136Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.14434","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3476e6f8f220f58db33cb828ac4e2c4a6f1943a00235d880ecdaed276932d181","sha256:b7b2c6e59c00e1c56624a42d476baeb419d83074bade4e94c3bdec7321cba792"],"state_sha256":"d40af14bc1fc038c0578e0f4132cc9d24168cc793e8f8d9bce7619c35a534449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YErn2YV/iHnzeoPd8Ianv2/iv+Lb9AMcZVWyMwTDmSZK7IaS8pAgRi+4CjEGW5eo0sVsaS1XIG1k41cLj4H7AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:04:45.686596Z","bundle_sha256":"bfa84e4f1ec93c251d6805457b7a19b22cb04babfff4ef1bf165bb9c624dec09"}}