{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KWCJEUMCWEYTWLLK2XDVMXYNCP","short_pith_number":"pith:KWCJEUMC","canonical_record":{"source":{"id":"1805.04784","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-12T21:12:20Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"14be67c5990546925c799af44dfa8f35632981c6d1963b7a4317554fc8a37b6e","abstract_canon_sha256":"9a5bed445fde0810b94f3d5d6b7cd9393de60d0b9eabb40e77ed0b633780ada8"},"schema_version":"1.0"},"canonical_sha256":"5584925182b1313b2d6ad5c7565f0d13cd0db3119436d96decf84c4964104810","source":{"kind":"arxiv","id":"1805.04784","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04784","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04784v3","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04784","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"KWCJEUMCWEYT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KWCJEUMCWEYTWLLK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KWCJEUMC","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KWCJEUMCWEYTWLLK2XDVMXYNCP","target":"record","payload":{"canonical_record":{"source":{"id":"1805.04784","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-12T21:12:20Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"14be67c5990546925c799af44dfa8f35632981c6d1963b7a4317554fc8a37b6e","abstract_canon_sha256":"9a5bed445fde0810b94f3d5d6b7cd9393de60d0b9eabb40e77ed0b633780ada8"},"schema_version":"1.0"},"canonical_sha256":"5584925182b1313b2d6ad5c7565f0d13cd0db3119436d96decf84c4964104810","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:49.366255Z","signature_b64":"Les5670FD0nJ952YvogPr9qznTf9eOCoEn+/RHHld9wful1rJ0MA3tS//ZblWaehNYZ4s/IELdTsagpMdLyRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5584925182b1313b2d6ad5c7565f0d13cd0db3119436d96decf84c4964104810","last_reissued_at":"2026-05-18T00:15:49.365561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:49.365561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.04784","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64gUq0hLXU8qwpTFGREu11sWxdauh72iaKwIqj+PtRMTA9eU03TTy/SJ11gkLxBf0WzMZ8Ld8vtDNrJAjM1/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:15:39.956629Z"},"content_sha256":"619dc9c0c1aeb00cb0e9cc725fd56744fe29f9ddfff274741476b052500e9215","schema_version":"1.0","event_id":"sha256:619dc9c0c1aeb00cb0e9cc725fd56744fe29f9ddfff274741476b052500e9215"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KWCJEUMCWEYTWLLK2XDVMXYNCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Metric Learning through Geodesic Interpolation within Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Bibo Shi, Charles D. Smith, Jundong Liu, Zhewei Wang","submitted_at":"2018-05-12T21:12:20Z","abstract_excerpt":"In this paper, we propose a nonlinear distance metric learning scheme based on the fusion of component linear metrics. Instead of merging displacements at each data point, our model calculates the velocities induced by the component transformations, via a geodesic interpolation on a Lie transfor- mation group. Such velocities are later summed up to produce a global transformation that is guaranteed to be diffeomorphic. Consequently, pair-wise distances computed this way conform to a smooth and spatially varying metric, which can greatly benefit k-NN classification. Experiments on synthetic and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04784","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ax3Mmtyg5em6cuZaV0I6Brfa/1fhl7rmQiGCdXdTHlvfLl3g7Bf3nKLYuACWmcUpqLLpg9wLQ9SBL33gHE5YBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:15:39.957304Z"},"content_sha256":"71f5fb4e1b9498132ee951c0dc24b41fec50a8bb43b06cb1c6e89f7c2ce2cecf","schema_version":"1.0","event_id":"sha256:71f5fb4e1b9498132ee951c0dc24b41fec50a8bb43b06cb1c6e89f7c2ce2cecf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/bundle.json","state_url":"https://pith.science/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T23:15:39Z","links":{"resolver":"https://pith.science/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP","bundle":"https://pith.science/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/bundle.json","state":"https://pith.science/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWCJEUMCWEYTWLLK2XDVMXYNCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KWCJEUMCWEYTWLLK2XDVMXYNCP","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":"9a5bed445fde0810b94f3d5d6b7cd9393de60d0b9eabb40e77ed0b633780ada8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-12T21:12:20Z","title_canon_sha256":"14be67c5990546925c799af44dfa8f35632981c6d1963b7a4317554fc8a37b6e"},"schema_version":"1.0","source":{"id":"1805.04784","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04784","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04784v3","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04784","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"KWCJEUMCWEYT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KWCJEUMCWEYTWLLK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KWCJEUMC","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:71f5fb4e1b9498132ee951c0dc24b41fec50a8bb43b06cb1c6e89f7c2ce2cecf","target":"graph","created_at":"2026-05-18T00:15:49Z","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 propose a nonlinear distance metric learning scheme based on the fusion of component linear metrics. Instead of merging displacements at each data point, our model calculates the velocities induced by the component transformations, via a geodesic interpolation on a Lie transfor- mation group. Such velocities are later summed up to produce a global transformation that is guaranteed to be diffeomorphic. Consequently, pair-wise distances computed this way conform to a smooth and spatially varying metric, which can greatly benefit k-NN classification. Experiments on synthetic and","authors_text":"Bibo Shi, Charles D. Smith, Jundong Liu, Zhewei Wang","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-12T21:12:20Z","title":"Nonlinear Metric Learning through Geodesic Interpolation within Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04784","kind":"arxiv","version":3},"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":"sha256:619dc9c0c1aeb00cb0e9cc725fd56744fe29f9ddfff274741476b052500e9215","target":"record","created_at":"2026-05-18T00:15:49Z","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":"9a5bed445fde0810b94f3d5d6b7cd9393de60d0b9eabb40e77ed0b633780ada8","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-05-12T21:12:20Z","title_canon_sha256":"14be67c5990546925c799af44dfa8f35632981c6d1963b7a4317554fc8a37b6e"},"schema_version":"1.0","source":{"id":"1805.04784","kind":"arxiv","version":3}},"canonical_sha256":"5584925182b1313b2d6ad5c7565f0d13cd0db3119436d96decf84c4964104810","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5584925182b1313b2d6ad5c7565f0d13cd0db3119436d96decf84c4964104810","first_computed_at":"2026-05-18T00:15:49.365561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:49.365561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Les5670FD0nJ952YvogPr9qznTf9eOCoEn+/RHHld9wful1rJ0MA3tS//ZblWaehNYZ4s/IELdTsagpMdLyRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:49.366255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04784","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:619dc9c0c1aeb00cb0e9cc725fd56744fe29f9ddfff274741476b052500e9215","sha256:71f5fb4e1b9498132ee951c0dc24b41fec50a8bb43b06cb1c6e89f7c2ce2cecf"],"state_sha256":"ba882c3f559d6f4b0917358c9a35b3b93c4ba8fb6cd67e4391a10525bd26c8c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2kF78is2TpGdEIX21yN3YEkcBaJ61ycPa25p/246cdShEaZ1N/LELsyT7FZl3VzHK/GHTJ3riOfjAQdTKvwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:15:39.960128Z","bundle_sha256":"7b954d6489dac7864fe28288c74a866ca4eb1e874e24f7ef04c3f87dd764c956"}}