{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FEG53AYQG5EQ6JSC4FDXXNYYU2","short_pith_number":"pith:FEG53AYQ","schema_version":"1.0","canonical_sha256":"290ddd831037490f2642e1477bb718a6be16154f8d24f778db726fc8712ed850","source":{"kind":"arxiv","id":"1608.04914","version":1},"attestation_state":"computed","paper":{"title":"Geometry-aware Similarity Learning on SPD Manifolds for Visual Recognition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Luc Van Gool, Ruiping Wang, Shiguang Shan, Wenxian Liu, Xianqiu Li, Xilin Chen, Zhiwu Huang","submitted_at":"2016-08-17T10:02:57Z","abstract_excerpt":"Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the underlying SPD manifold. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly pursuing manifold-manifold transformation matrix of column full-rank. Specifically, by exploiting the Riemannian geometry of the manifold of fixed-rank Positive Semidefinite (PSD) matrices, we present a "},"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":"1608.04914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-08-17T10:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"2f832885b9f585b6fdb818c71c3b4f85d1d1ac776c6d46a5e6da23525e849b42","abstract_canon_sha256":"31b299f27613cae7afe840ae9f7eb5cb93cad31852bcc3dbd81951a640fee2be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:33.263812Z","signature_b64":"CrGRGDuMzkVm1sDXWAYh2MkSXyo7Z166JpCoXAfeWQZK1IKgBkfMz07Qq43nMFxjByXeGBAgUwztJ1cbgoQ8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"290ddd831037490f2642e1477bb718a6be16154f8d24f778db726fc8712ed850","last_reissued_at":"2026-05-18T01:08:33.263172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:33.263172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry-aware Similarity Learning on SPD Manifolds for Visual Recognition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Luc Van Gool, Ruiping Wang, Shiguang Shan, Wenxian Liu, Xianqiu Li, Xilin Chen, Zhiwu Huang","submitted_at":"2016-08-17T10:02:57Z","abstract_excerpt":"Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the underlying SPD manifold. In this paper, we propose a geometry-aware SPD similarity learning (SPDSL) framework to learn discriminative SPD features by directly pursuing manifold-manifold transformation matrix of column full-rank. Specifically, by exploiting the Riemannian geometry of the manifold of fixed-rank Positive Semidefinite (PSD) matrices, we present a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04914","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":"1608.04914","created_at":"2026-05-18T01:08:33.263297+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04914v1","created_at":"2026-05-18T01:08:33.263297+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04914","created_at":"2026-05-18T01:08:33.263297+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEG53AYQG5EQ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEG53AYQG5EQ6JSC","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEG53AYQ","created_at":"2026-05-18T12:30:15.759754+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/FEG53AYQG5EQ6JSC4FDXXNYYU2","json":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2.json","graph_json":"https://pith.science/api/pith-number/FEG53AYQG5EQ6JSC4FDXXNYYU2/graph.json","events_json":"https://pith.science/api/pith-number/FEG53AYQG5EQ6JSC4FDXXNYYU2/events.json","paper":"https://pith.science/paper/FEG53AYQ"},"agent_actions":{"view_html":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2","download_json":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2.json","view_paper":"https://pith.science/paper/FEG53AYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04914&json=true","fetch_graph":"https://pith.science/api/pith-number/FEG53AYQG5EQ6JSC4FDXXNYYU2/graph.json","fetch_events":"https://pith.science/api/pith-number/FEG53AYQG5EQ6JSC4FDXXNYYU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2/action/storage_attestation","attest_author":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2/action/author_attestation","sign_citation":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2/action/citation_signature","submit_replication":"https://pith.science/pith/FEG53AYQG5EQ6JSC4FDXXNYYU2/action/replication_record"}},"created_at":"2026-05-18T01:08:33.263297+00:00","updated_at":"2026-05-18T01:08:33.263297+00:00"}