{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L4COXGFTTJ6BMTFYDJISIL2KVQ","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":"418c379aea881884be88ef3d878a2ca959fa810f8630f932321f20832357ee96","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-01-15T15:59:46Z","title_canon_sha256":"6ea93d797d9028f01b67f218d701597c839ad0c0953007f4c442ba8b577580c0"},"schema_version":"1.0","source":{"id":"1301.3389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3389","created_at":"2026-05-18T03:30:41Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3389v2","created_at":"2026-05-18T03:30:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3389","created_at":"2026-05-18T03:30:41Z"},{"alias_kind":"pith_short_12","alias_value":"L4COXGFTTJ6B","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L4COXGFTTJ6BMTFY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L4COXGFT","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:0e8fbc98681e4a8eada6e36bef65974ba86da5f594b57aa7ca7342a779c725ce","target":"graph","created_at":"2026-05-18T03:30:41Z","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) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF","authors_text":"Hugo Van hamme","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-01-15T15:59:46Z","title":"The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3389","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:ffbe7091525f13fe58688f26b0c25d1e632ec36de2af8cf650068633084428ca","target":"record","created_at":"2026-05-18T03:30:41Z","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":"418c379aea881884be88ef3d878a2ca959fa810f8630f932321f20832357ee96","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-01-15T15:59:46Z","title_canon_sha256":"6ea93d797d9028f01b67f218d701597c839ad0c0953007f4c442ba8b577580c0"},"schema_version":"1.0","source":{"id":"1301.3389","kind":"arxiv","version":2}},"canonical_sha256":"5f04eb98b39a7c164cb81a51242f4aac215b520ada8989609c0a1ecfb971db83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f04eb98b39a7c164cb81a51242f4aac215b520ada8989609c0a1ecfb971db83","first_computed_at":"2026-05-18T03:30:41.052793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:41.052793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6heJUfBSBEa5/uaeK6ZIm+z95gX1gzK393/+SAirpOlLWHU+gjk4EPku11/nttIUsRBKgyiExF6rK7dvfzuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:41.053607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffbe7091525f13fe58688f26b0c25d1e632ec36de2af8cf650068633084428ca","sha256:0e8fbc98681e4a8eada6e36bef65974ba86da5f594b57aa7ca7342a779c725ce"],"state_sha256":"2d1e370082f6e058d78761efd5b58296d1bd605ac7d73dd906998eb10b00f480"}