{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UNZBI6NX2J2PHLUGVAT5CMG3TD","short_pith_number":"pith:UNZBI6NX","canonical_record":{"source":{"id":"1612.04112","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-13T12:02:24Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"2ee5c7c3f43cee1bf2a56d9cd56f141f914d300cac9fc7446ebe83a034e5b045","abstract_canon_sha256":"91f25bb4c4e8963f1c74e6e1fe1849a406bf0853df728bf22de307846350be52"},"schema_version":"1.0"},"canonical_sha256":"a3721479b7d274f3ae86a827d130db98d00ab61d30687c513a85cd55225b9774","source":{"kind":"arxiv","id":"1612.04112","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04112","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04112v5","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04112","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"UNZBI6NX2J2P","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNZBI6NX2J2PHLUG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNZBI6NX","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UNZBI6NX2J2PHLUGVAT5CMG3TD","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04112","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-13T12:02:24Z","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"title_canon_sha256":"2ee5c7c3f43cee1bf2a56d9cd56f141f914d300cac9fc7446ebe83a034e5b045","abstract_canon_sha256":"91f25bb4c4e8963f1c74e6e1fe1849a406bf0853df728bf22de307846350be52"},"schema_version":"1.0"},"canonical_sha256":"a3721479b7d274f3ae86a827d130db98d00ab61d30687c513a85cd55225b9774","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:56.990380Z","signature_b64":"kQAk0lh+56ew1sETKzlBz0requfbOGrodHh3A4bHMfqRGt8SiRImN3y9lMwFEfcwnLXPML01eanb4oobeqKpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3721479b7d274f3ae86a827d130db98d00ab61d30687c513a85cd55225b9774","last_reissued_at":"2026-05-17T23:43:56.989585Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:56.989585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04112","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+kwzLqXVmqwWLOPnyllQkn4mtnScSi0w9Ie55o5oPcWmqZFHfkdr6Dhc7DsgwXSScgNC7sqZ8amJKkG2fzbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:23:09.370844Z"},"content_sha256":"b450a58bca3676cdce73ee7e61bc582000c076a9adce56f030573f692c4b70e9","schema_version":"1.0","event_id":"sha256:b450a58bca3676cdce73ee7e61bc582000c076a9adce56f030573f692c4b70e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UNZBI6NX2J2PHLUGVAT5CMG3TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Naoki Hayashi, Sumio Watanabe","submitted_at":"2016-12-13T12:02:24Z","abstract_excerpt":"Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log canonical threshold of NMF and give an upper bound of the generalization error in Bayesian learning. The results show that the generalization error of the matrix factorization can be made smaller than regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04112","kind":"arxiv","version":5},"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":"2026-05-17T23:43:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6SyPjKlsEDj4ZgNhMGDwmCIUmNZOmo/u6BVw+LQKpjALamAXlxKdwm/qqWBgSEpl7CKOZIxJGT9c/1WY2SrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:23:09.371263Z"},"content_sha256":"8d3736762aa1b1c0c89c3fb8c1438f02604125e02e56b0d776b1ddf549879e39","schema_version":"1.0","event_id":"sha256:8d3736762aa1b1c0c89c3fb8c1438f02604125e02e56b0d776b1ddf549879e39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/bundle.json","state_url":"https://pith.science/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/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":"2026-06-04T19:23:09Z","links":{"resolver":"https://pith.science/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD","bundle":"https://pith.science/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/bundle.json","state":"https://pith.science/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNZBI6NX2J2PHLUGVAT5CMG3TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UNZBI6NX2J2PHLUGVAT5CMG3TD","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":"91f25bb4c4e8963f1c74e6e1fe1849a406bf0853df728bf22de307846350be52","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-13T12:02:24Z","title_canon_sha256":"2ee5c7c3f43cee1bf2a56d9cd56f141f914d300cac9fc7446ebe83a034e5b045"},"schema_version":"1.0","source":{"id":"1612.04112","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04112","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04112v5","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04112","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"UNZBI6NX2J2P","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNZBI6NX2J2PHLUG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNZBI6NX","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:8d3736762aa1b1c0c89c3fb8c1438f02604125e02e56b0d776b1ddf549879e39","target":"graph","created_at":"2026-05-17T23:43:56Z","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":"Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log canonical threshold of NMF and give an upper bound of the generalization error in Bayesian learning. The results show that the generalization error of the matrix factorization can be made smaller than regul","authors_text":"Naoki Hayashi, Sumio Watanabe","cross_cats":["cs.LG","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-13T12:02:24Z","title":"Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04112","kind":"arxiv","version":5},"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:b450a58bca3676cdce73ee7e61bc582000c076a9adce56f030573f692c4b70e9","target":"record","created_at":"2026-05-17T23:43:56Z","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":"91f25bb4c4e8963f1c74e6e1fe1849a406bf0853df728bf22de307846350be52","cross_cats_sorted":["cs.LG","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-13T12:02:24Z","title_canon_sha256":"2ee5c7c3f43cee1bf2a56d9cd56f141f914d300cac9fc7446ebe83a034e5b045"},"schema_version":"1.0","source":{"id":"1612.04112","kind":"arxiv","version":5}},"canonical_sha256":"a3721479b7d274f3ae86a827d130db98d00ab61d30687c513a85cd55225b9774","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3721479b7d274f3ae86a827d130db98d00ab61d30687c513a85cd55225b9774","first_computed_at":"2026-05-17T23:43:56.989585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:56.989585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQAk0lh+56ew1sETKzlBz0requfbOGrodHh3A4bHMfqRGt8SiRImN3y9lMwFEfcwnLXPML01eanb4oobeqKpAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:56.990380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04112","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b450a58bca3676cdce73ee7e61bc582000c076a9adce56f030573f692c4b70e9","sha256:8d3736762aa1b1c0c89c3fb8c1438f02604125e02e56b0d776b1ddf549879e39"],"state_sha256":"840db84bd700756bce7ea2af67954f95d39d8a1e330c47da6fa29148b073868d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xvevJis9+UX2DiQEeh8kRONqTpluaVRWcGPBZ1Y7Mj3HEAvI7HwlgPYt5hjY9slJL5BnCm4z2MIYIOIUWGPODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:23:09.373571Z","bundle_sha256":"e2db49147b0df2a0215c9c30d362efb97f0e58967d92c743a91c795cd4e0a64b"}}