{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MO2KHWOWX2QF54IEGSVQHMR6Q5","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":"9858b7790647016b3d8ec6a11a4d179742ee7bf79081c13b83b7183f5a9e93fd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-08-28T11:22:08Z","title_canon_sha256":"ac3d55c4c1cd78794def1a3a600d5c9227e11ba017b677e380abd7c9f66909d6"},"schema_version":"1.0","source":{"id":"1408.6686","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6686","created_at":"2026-05-18T01:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6686v2","created_at":"2026-05-18T01:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6686","created_at":"2026-05-18T01:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"MO2KHWOWX2QF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MO2KHWOWX2QF54IE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MO2KHWOW","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:004479565184f77cfc8058e44f87650b35f05f4b271ca4a9e10791d8519655e0","target":"graph","created_at":"2026-05-18T01:42:12Z","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 paper, we consider an $\\ell_{0}$-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is therefore computationally intractable. To tackle the problem, we first approximate the $\\ell_{0}$-norm by a continuous surrogate function. Then an algorithm is developed via iteratively majorizing the surrogate function by a quadratic separable function, which at each iteration ","authors_text":"Daniel P. Palomar, Junxiao Song, Prabhu Babu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-08-28T11:22:08Z","title":"Sparse Generalized Eigenvalue Problem via Smooth Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6686","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:e1a3f9af58c0221dcbf62ccaf362a8d44c18799a817e2e185e824950e39a85a9","target":"record","created_at":"2026-05-18T01:42:12Z","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":"9858b7790647016b3d8ec6a11a4d179742ee7bf79081c13b83b7183f5a9e93fd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-08-28T11:22:08Z","title_canon_sha256":"ac3d55c4c1cd78794def1a3a600d5c9227e11ba017b677e380abd7c9f66909d6"},"schema_version":"1.0","source":{"id":"1408.6686","kind":"arxiv","version":2}},"canonical_sha256":"63b4a3d9d6bea05ef10434ab03b23e877841376f101aae7e80705f0c8e40031e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63b4a3d9d6bea05ef10434ab03b23e877841376f101aae7e80705f0c8e40031e","first_computed_at":"2026-05-18T01:42:12.307716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:12.307716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OG0By1aY//T0ididNqbnCpguijkG8WKzVRcXOpr4SsYFlaEsrt5nrXk2lx0FZ6vSuHlDuIj3CHfwkRim1rRuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:12.308300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6686","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1a3f9af58c0221dcbf62ccaf362a8d44c18799a817e2e185e824950e39a85a9","sha256:004479565184f77cfc8058e44f87650b35f05f4b271ca4a9e10791d8519655e0"],"state_sha256":"4c933a25c1dc8fbbaa253c14056ba2b42b190c61e0534f8c904503973ae7a731"}