{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NDPSEJDIZM2LMFKF7UAEBA6SV6","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":"c5296e335fafbd9c706a9e43c93fb2d246bb147d72c5ded9b051ab35ac347d61","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-01-15T23:11:05Z","title_canon_sha256":"33e6ed20bf46e64364ddd25fafd51d666473e7394737bff9b69fc92d37f9148d"},"schema_version":"1.0","source":{"id":"1301.3527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3527","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3527v2","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3527","created_at":"2026-05-18T03:30:27Z"},{"alias_kind":"pith_short_12","alias_value":"NDPSEJDIZM2L","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NDPSEJDIZM2LMFKF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NDPSEJDI","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:2708ca1bcd75960942215563f638fb55b58fe28798604e8f0ea849cb99c8bd2e","target":"graph","created_at":"2026-05-18T03:30:27Z","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":"Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed no","authors_text":"Barak A. Pearlmutter, Jonathan Le Roux, Sergey M. Plis, Thomas P. Hayes, Vamsi K. Potluru, Vince D. Calhoun","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-01-15T23:11:05Z","title":"Block Coordinate Descent for Sparse NMF"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3527","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":"sha256:5752f7929d8c0b07d7ab34e4c71f66b28d9e88663015aa211b2a0e2f209aef2c","target":"record","created_at":"2026-05-18T03:30:27Z","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":"c5296e335fafbd9c706a9e43c93fb2d246bb147d72c5ded9b051ab35ac347d61","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-01-15T23:11:05Z","title_canon_sha256":"33e6ed20bf46e64364ddd25fafd51d666473e7394737bff9b69fc92d37f9148d"},"schema_version":"1.0","source":{"id":"1301.3527","kind":"arxiv","version":2}},"canonical_sha256":"68df222468cb34b61545fd004083d2af958a3a3739eb84b5b13cc3172fd3d4fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68df222468cb34b61545fd004083d2af958a3a3739eb84b5b13cc3172fd3d4fb","first_computed_at":"2026-05-18T03:30:27.538828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:27.538828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgCLT+ywtwjxDAXRJBMDov3XfEIn+az6Ij3rU8o2FWlj4+3JNAcBglbZbN0c/58IqJXm31kO/fXjdCJRYjNSDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:27.539601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5752f7929d8c0b07d7ab34e4c71f66b28d9e88663015aa211b2a0e2f209aef2c","sha256:2708ca1bcd75960942215563f638fb55b58fe28798604e8f0ea849cb99c8bd2e"],"state_sha256":"fc84b13a32d85400fcd3968e9b5e4ef04a080bf2c59c0db91ded6f74cc794dcc"}