{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K3HJG4SU6NMPWAQ64TTOKR2FPG","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":"c3c6ae5cf36c127bb9789c7b34f9c199115bcdf1c7d99c977798ea24966ff2e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-11-30T19:25:20Z","title_canon_sha256":"fe31dbfe9e8ea3e7416870b590e4c4f7e0e08e2939462e97bafe0aaf07bf9a8a"},"schema_version":"1.0","source":{"id":"1412.0265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0265","created_at":"2026-05-18T02:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0265v2","created_at":"2026-05-18T02:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0265","created_at":"2026-05-18T02:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"K3HJG4SU6NMP","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K3HJG4SU6NMPWAQ6","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K3HJG4SU","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:d0f3e25f84cec35cc161e7255997a9429b85f29e8fcd0aa246f968604f4d55fa","target":"graph","created_at":"2026-05-18T02:22:29Z","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 develop an approach to exploiting kernel methods with manifold-valued data. In many computer vision problems, the data can be naturally represented as points on a Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, usual Euclidean computer vision and machine learning algorithms yield inferior results on such data. In this paper, we define Gaussian radial basis function (RBF)-based positive definite kernels on manifolds that permit us to embed a given manifold with a corresponding metric in a high dimensional reproducing kernel Hilbert space. These ","authors_text":"Hongdong Li, Mathieu Salzmann, Mehrtash Harandi, Richard Hartley, Sadeep Jayasumana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-11-30T19:25:20Z","title":"Kernel Methods on Riemannian Manifolds with Gaussian RBF Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0265","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":"sha256:1111c47d0eec77ab34cc8de6a3a66ef74d6a3898b3a951d4bfab6fd81a5447ef","target":"record","created_at":"2026-05-18T02:22:29Z","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":"c3c6ae5cf36c127bb9789c7b34f9c199115bcdf1c7d99c977798ea24966ff2e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-11-30T19:25:20Z","title_canon_sha256":"fe31dbfe9e8ea3e7416870b590e4c4f7e0e08e2939462e97bafe0aaf07bf9a8a"},"schema_version":"1.0","source":{"id":"1412.0265","kind":"arxiv","version":2}},"canonical_sha256":"56ce937254f358fb021ee4e6e547457992b85bcdae126b86f3c409d9e8de03b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56ce937254f358fb021ee4e6e547457992b85bcdae126b86f3c409d9e8de03b7","first_computed_at":"2026-05-18T02:22:29.019622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:29.019622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"su/VbeVOAm0LFS6nxB3L1arXg/kNevxDqos315LB5hkBUNo+nSL5WB6Zv8nv4L06uQTBaX9d4SwrL2sSWb2iCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:29.020361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1111c47d0eec77ab34cc8de6a3a66ef74d6a3898b3a951d4bfab6fd81a5447ef","sha256:d0f3e25f84cec35cc161e7255997a9429b85f29e8fcd0aa246f968604f4d55fa"],"state_sha256":"4f2813c1164a05eb6a4557301ecd8dceeb5d99e126e1e569c1fcfc89e6e57e4f"}