{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T6ZRH2SLDWEYL72KNF5P4IQIFO","short_pith_number":"pith:T6ZRH2SL","canonical_record":{"source":{"id":"1507.00333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-30T20:47:34Z","cross_cats_sorted":["cs.IR","cs.LG"],"title_canon_sha256":"cf20b64eb2baa732ae3807f662f884f5bf4406b1af7baad76b5546d6108dc968","abstract_canon_sha256":"42fa3a1fc886140391b77dfd11f36400ca845bbd0d7ef0cb57ad7ea2f7bbcba1"},"schema_version":"1.0"},"canonical_sha256":"9fb313ea4b1d8985ff4a697afe22082b846024bc801978bab23a62f33543dca4","source":{"kind":"arxiv","id":"1507.00333","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00333","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00333v3","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00333","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"T6ZRH2SLDWEY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T6ZRH2SLDWEYL72K","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T6ZRH2SL","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T6ZRH2SLDWEYL72KNF5P4IQIFO","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-30T20:47:34Z","cross_cats_sorted":["cs.IR","cs.LG"],"title_canon_sha256":"cf20b64eb2baa732ae3807f662f884f5bf4406b1af7baad76b5546d6108dc968","abstract_canon_sha256":"42fa3a1fc886140391b77dfd11f36400ca845bbd0d7ef0cb57ad7ea2f7bbcba1"},"schema_version":"1.0"},"canonical_sha256":"9fb313ea4b1d8985ff4a697afe22082b846024bc801978bab23a62f33543dca4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:32.518403Z","signature_b64":"Hmyqs8nAZZ8F9Bgb5qUiuIy8QXWbDJ4QSp5pC4nyBz92q4EujX4IZnT68hbulpP5xyGCxOLSG/8AlFno6xr3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb313ea4b1d8985ff4a697afe22082b846024bc801978bab23a62f33543dca4","last_reissued_at":"2026-05-18T01:15:32.517747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:32.517747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00333","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ku8dhgzYKi5IGxKTqbkbuSMBdEVv5Iox7idFYd7fTdI5m/Xy9+G+xPWQ6S/qkf+Gr4nGaJ7+crCeIbjyH0umBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:29:23.878262Z"},"content_sha256":"92dd7fe9f435081b12e8110162d0f8b6bc181b49e528ee04ca74ed8b08c1cec0","schema_version":"1.0","event_id":"sha256:92dd7fe9f435081b12e8110162d0f8b6bc181b49e528ee04ca74ed8b08c1cec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T6ZRH2SLDWEYL72KNF5P4IQIFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on Low-rank Matrix Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IR","cs.LG"],"primary_cat":"cs.NA","authors_text":"Jie Yang, Yuan Lu","submitted_at":"2015-06-30T20:47:34Z","abstract_excerpt":"Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimension reduction, clustering, and matrix completion. In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be told from their names, non-negative MF and orthogonal non-negative MF are variants of basic M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00333","kind":"arxiv","version":3},"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":"2026-05-18T01:15:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7hGAqNr+ypf9cczLeK+hXz3boPLSLqmAQpYEj+LcpFl8CMOU5tmknR3Ch+LsV6Q5Sm816uPB+8kvOlLy+rdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:29:23.878830Z"},"content_sha256":"69379f0a969233c4e794805185ade6d4c992050ab2de8b2648730539b210c748","schema_version":"1.0","event_id":"sha256:69379f0a969233c4e794805185ade6d4c992050ab2de8b2648730539b210c748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/bundle.json","state_url":"https://pith.science/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/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":"2026-08-08T21:29:23Z","links":{"resolver":"https://pith.science/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO","bundle":"https://pith.science/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/bundle.json","state":"https://pith.science/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6ZRH2SLDWEYL72KNF5P4IQIFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T6ZRH2SLDWEYL72KNF5P4IQIFO","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":"42fa3a1fc886140391b77dfd11f36400ca845bbd0d7ef0cb57ad7ea2f7bbcba1","cross_cats_sorted":["cs.IR","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-30T20:47:34Z","title_canon_sha256":"cf20b64eb2baa732ae3807f662f884f5bf4406b1af7baad76b5546d6108dc968"},"schema_version":"1.0","source":{"id":"1507.00333","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00333","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00333v3","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00333","created_at":"2026-05-18T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"T6ZRH2SLDWEY","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T6ZRH2SLDWEYL72K","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T6ZRH2SL","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:69379f0a969233c4e794805185ade6d4c992050ab2de8b2648730539b210c748","target":"graph","created_at":"2026-05-18T01:15:32Z","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":"Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimension reduction, clustering, and matrix completion. In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be told from their names, non-negative MF and orthogonal non-negative MF are variants of basic M","authors_text":"Jie Yang, Yuan Lu","cross_cats":["cs.IR","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-30T20:47:34Z","title":"Notes on Low-rank Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00333","kind":"arxiv","version":3},"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":"sha256:92dd7fe9f435081b12e8110162d0f8b6bc181b49e528ee04ca74ed8b08c1cec0","target":"record","created_at":"2026-05-18T01:15:32Z","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":"42fa3a1fc886140391b77dfd11f36400ca845bbd0d7ef0cb57ad7ea2f7bbcba1","cross_cats_sorted":["cs.IR","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-06-30T20:47:34Z","title_canon_sha256":"cf20b64eb2baa732ae3807f662f884f5bf4406b1af7baad76b5546d6108dc968"},"schema_version":"1.0","source":{"id":"1507.00333","kind":"arxiv","version":3}},"canonical_sha256":"9fb313ea4b1d8985ff4a697afe22082b846024bc801978bab23a62f33543dca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fb313ea4b1d8985ff4a697afe22082b846024bc801978bab23a62f33543dca4","first_computed_at":"2026-05-18T01:15:32.517747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:32.517747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hmyqs8nAZZ8F9Bgb5qUiuIy8QXWbDJ4QSp5pC4nyBz92q4EujX4IZnT68hbulpP5xyGCxOLSG/8AlFno6xr3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:32.518403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00333","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92dd7fe9f435081b12e8110162d0f8b6bc181b49e528ee04ca74ed8b08c1cec0","sha256:69379f0a969233c4e794805185ade6d4c992050ab2de8b2648730539b210c748"],"state_sha256":"b3a2f5ea4e102080623148de4599b081a50512bf750433176ba1f76c03e5a676"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIQbe4r4FYcgvXuzDvQ1AotKqZw4FZCdod+9xQe293JulTci5d6NeCRPtfeemgY0BUwFAGmKC2NueuVjUvQ8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T21:29:23.882867Z","bundle_sha256":"a78ce8829016f4dc2611efde78283f402500d3b76dc1f043e92b07f50ed5ee2c"}}