{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:27P3OKNVMCZRGCHVQFKHE6VFJT","short_pith_number":"pith:27P3OKNV","canonical_record":{"source":{"id":"1803.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T08:11:07Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"f5ef02e54cd960d2d2843a3294fc3d7215bb65fe214ed85e9cbf22794681b478","abstract_canon_sha256":"bbd737ee588461a8ff461168ace0f31010f8aa84cd198fb3ad4100ef3f580668"},"schema_version":"1.0"},"canonical_sha256":"d7dfb729b560b31308f58154727aa54cc690f063e7f3912e682435c1c8db41e2","source":{"kind":"arxiv","id":"1803.05159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05159","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05159v2","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05159","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"pith_short_12","alias_value":"27P3OKNVMCZR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"27P3OKNVMCZRGCHV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"27P3OKNV","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:27P3OKNVMCZRGCHVQFKHE6VFJT","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T08:11:07Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"f5ef02e54cd960d2d2843a3294fc3d7215bb65fe214ed85e9cbf22794681b478","abstract_canon_sha256":"bbd737ee588461a8ff461168ace0f31010f8aa84cd198fb3ad4100ef3f580668"},"schema_version":"1.0"},"canonical_sha256":"d7dfb729b560b31308f58154727aa54cc690f063e7f3912e682435c1c8db41e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:51.371520Z","signature_b64":"8wRj+vQ/eME0nVkhT06JMtoJPd9AcWlY5tjNWXu/r2pEOrn9h0GUDpckUk0e+JtMhpQq8cDrKUMtjS9Lo/zZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7dfb729b560b31308f58154727aa54cc690f063e7f3912e682435c1c8db41e2","last_reissued_at":"2026-05-17T23:43:51.370882Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:51.370882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05159","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Gtufdy2wffTYq3D+6CKWJNHQeVphnBps2AEB2Ge6PKWSqfSgzzc/VKHj+bTfdIo/AGlTWU+xqKoLt8ZZwKgAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:14:37.978614Z"},"content_sha256":"316d12c0bf5fadedabe09fad2ddd720981c6e8c1982068068d35b489897a2573","schema_version":"1.0","event_id":"sha256:316d12c0bf5fadedabe09fad2ddd720981c6e8c1982068068d35b489897a2573"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:27P3OKNVMCZRGCHVQFKHE6VFJT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicative Updates for Convolutional NMF Under $\\beta$-Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Arvind T. Hariraman, Pedro J. Villasana T., Stanislaw Gorlow","submitted_at":"2018-03-14T08:11:07Z","abstract_excerpt":"In this letter, we generalize the convolutional NMF by taking the $\\beta$-divergence as the contrast function and present the correct multiplicative updates for its factors in closed form. The new updates unify the $\\beta$-NMF and the convolutional NMF. We state why almost all of the existing updates are inexact and approximative w.r.t. the convolutional data model. We show that our updates are stable and that their convergence performance is consistent across the most common values of $\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05159","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:43:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIWSTBaRS1A3daX3iyB53RwQD33oogrWW7UTxYbJ8q2w5T4ir4AsQvsbdZXFcmgas+JLh5xpiyawiy4Itxm/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:14:37.979291Z"},"content_sha256":"93d68761d4fbb5b984ff544bf69232e760ac26eeb082ef6432345814464d78ea","schema_version":"1.0","event_id":"sha256:93d68761d4fbb5b984ff544bf69232e760ac26eeb082ef6432345814464d78ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/bundle.json","state_url":"https://pith.science/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/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":"2026-05-27T08:14:37Z","links":{"resolver":"https://pith.science/pith/27P3OKNVMCZRGCHVQFKHE6VFJT","bundle":"https://pith.science/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/bundle.json","state":"https://pith.science/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27P3OKNVMCZRGCHVQFKHE6VFJT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:27P3OKNVMCZRGCHVQFKHE6VFJT","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":"bbd737ee588461a8ff461168ace0f31010f8aa84cd198fb3ad4100ef3f580668","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T08:11:07Z","title_canon_sha256":"f5ef02e54cd960d2d2843a3294fc3d7215bb65fe214ed85e9cbf22794681b478"},"schema_version":"1.0","source":{"id":"1803.05159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05159","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05159v2","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05159","created_at":"2026-05-17T23:43:51Z"},{"alias_kind":"pith_short_12","alias_value":"27P3OKNVMCZR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"27P3OKNVMCZRGCHV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"27P3OKNV","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:93d68761d4fbb5b984ff544bf69232e760ac26eeb082ef6432345814464d78ea","target":"graph","created_at":"2026-05-17T23:43:51Z","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"},"paper":{"abstract_excerpt":"In this letter, we generalize the convolutional NMF by taking the $\\beta$-divergence as the contrast function and present the correct multiplicative updates for its factors in closed form. The new updates unify the $\\beta$-NMF and the convolutional NMF. We state why almost all of the existing updates are inexact and approximative w.r.t. the convolutional data model. We show that our updates are stable and that their convergence performance is consistent across the most common values of $\\beta$.","authors_text":"Arvind T. Hariraman, Pedro J. Villasana T., Stanislaw Gorlow","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T08:11:07Z","title":"Multiplicative Updates for Convolutional NMF Under $\\beta$-Divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05159","kind":"arxiv","version":2},"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":"sha256:316d12c0bf5fadedabe09fad2ddd720981c6e8c1982068068d35b489897a2573","target":"record","created_at":"2026-05-17T23:43:51Z","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":"bbd737ee588461a8ff461168ace0f31010f8aa84cd198fb3ad4100ef3f580668","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T08:11:07Z","title_canon_sha256":"f5ef02e54cd960d2d2843a3294fc3d7215bb65fe214ed85e9cbf22794681b478"},"schema_version":"1.0","source":{"id":"1803.05159","kind":"arxiv","version":2}},"canonical_sha256":"d7dfb729b560b31308f58154727aa54cc690f063e7f3912e682435c1c8db41e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7dfb729b560b31308f58154727aa54cc690f063e7f3912e682435c1c8db41e2","first_computed_at":"2026-05-17T23:43:51.370882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:51.370882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8wRj+vQ/eME0nVkhT06JMtoJPd9AcWlY5tjNWXu/r2pEOrn9h0GUDpckUk0e+JtMhpQq8cDrKUMtjS9Lo/zZDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:51.371520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:316d12c0bf5fadedabe09fad2ddd720981c6e8c1982068068d35b489897a2573","sha256:93d68761d4fbb5b984ff544bf69232e760ac26eeb082ef6432345814464d78ea"],"state_sha256":"92bf8e928d297dee28c5ace8e8ac1d3d3a34a54b7bd6acbbc0463b43ba566e75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6HAjzOCjdkeygCBrSqlz015m+fjyfPfBawq0m+Fow7PjXsRhpPJ7kVNUfIyBQujCMRa7oZ1MgEKZGQV/u7JBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:14:37.982781Z","bundle_sha256":"4239fe6a325620e213bed4eda442e162f51ab039a6ac9c64cc0617bc50f82a2d"}}