{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:C2QBFWVT3HHP5SPI6SAOIXFI7F","short_pith_number":"pith:C2QBFWVT","schema_version":"1.0","canonical_sha256":"16a012dab3d9cefec9e8f480e45ca8f964a06f6547112a299632ad561feb42e4","source":{"kind":"arxiv","id":"1607.05002","version":1},"attestation_state":"computed","paper":{"title":"Geometric Mean Metric Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Pourya Habib Zadeh, Reshad Hosseini, Suvrit Sra","submitted_at":"2016-07-18T10:14:46Z","abstract_excerpt":"We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution con"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.05002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-18T10:14:46Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"4ad089b73d9ae5f7693c1123ea4740ba1a35fa05973f6547923a8700e195ac02","abstract_canon_sha256":"224312e7aa93caeb257384af619b4a770f6218bcb84056b96a3f0109083216e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:56.145466Z","signature_b64":"Vt8l1EvMBXilCP6s1SCNE0rrCtdRBpgLlCb0sqtdjw98JuJmMAdhVWWMEjgmv2ysxfB13c6H4gq8p6JXZjPGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16a012dab3d9cefec9e8f480e45ca8f964a06f6547112a299632ad561feb42e4","last_reissued_at":"2026-05-18T01:10:56.145007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:56.145007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Mean Metric Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Pourya Habib Zadeh, Reshad Hosseini, Suvrit Sra","submitted_at":"2016-07-18T10:14:46Z","abstract_excerpt":"We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05002","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.05002","created_at":"2026-05-18T01:10:56.145081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05002v1","created_at":"2026-05-18T01:10:56.145081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05002","created_at":"2026-05-18T01:10:56.145081+00:00"},{"alias_kind":"pith_short_12","alias_value":"C2QBFWVT3HHP","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C2QBFWVT3HHP5SPI","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C2QBFWVT","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F","json":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F.json","graph_json":"https://pith.science/api/pith-number/C2QBFWVT3HHP5SPI6SAOIXFI7F/graph.json","events_json":"https://pith.science/api/pith-number/C2QBFWVT3HHP5SPI6SAOIXFI7F/events.json","paper":"https://pith.science/paper/C2QBFWVT"},"agent_actions":{"view_html":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F","download_json":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F.json","view_paper":"https://pith.science/paper/C2QBFWVT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05002&json=true","fetch_graph":"https://pith.science/api/pith-number/C2QBFWVT3HHP5SPI6SAOIXFI7F/graph.json","fetch_events":"https://pith.science/api/pith-number/C2QBFWVT3HHP5SPI6SAOIXFI7F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F/action/storage_attestation","attest_author":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F/action/author_attestation","sign_citation":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F/action/citation_signature","submit_replication":"https://pith.science/pith/C2QBFWVT3HHP5SPI6SAOIXFI7F/action/replication_record"}},"created_at":"2026-05-18T01:10:56.145081+00:00","updated_at":"2026-05-18T01:10:56.145081+00:00"}