{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S243R3W4ZOE46K2ED7UCUAEQYT","short_pith_number":"pith:S243R3W4","schema_version":"1.0","canonical_sha256":"96b9b8eedccb89cf2b441fe82a0090c4e872db504ba64fe6b8e11ec58cb4a84d","source":{"kind":"arxiv","id":"1806.09039","version":2},"attestation_state":"computed","paper":{"title":"Parallel Transport Unfolding: A Connection-based Manifold Learning Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Glorian Yin, Leman Feng, Mathieu Desbrun, Max Budninskiy, Yiying Tong","submitted_at":"2018-06-23T21:29:50Z","abstract_excerpt":"Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a quasi-isometric, low-dimensional mapping from a sparse and irregular sampling of an arbitrary manifold embedded in a high-dimensional space. Geodesic distances of discrete paths over the input pointset are evaluated through \"parallel transport unfolding\" (PTU) to offer robustness to poor sampling and arbitrary topology. Our new geometric procedure exhibits the "},"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":"1806.09039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-23T21:29:50Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"e3616d535639e549c18427d000bf39fdaa0049b067761b69e7444b9b9384362b","abstract_canon_sha256":"c2ceb91d1c5c0d9605fd2bd7b821ea96d4c192e6091b9111af9a7c14c7ea36ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:43.343436Z","signature_b64":"ia80ns1zgMBT0Ni+khTysKxIgLRhGx8nIYb7nBVhRD37z98/nl3EeztjFBgdOXRg2iWvCNluqUlMbhXU+sHaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b9b8eedccb89cf2b441fe82a0090c4e872db504ba64fe6b8e11ec58cb4a84d","last_reissued_at":"2026-05-18T00:01:43.342928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:43.342928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parallel Transport Unfolding: A Connection-based Manifold Learning Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Glorian Yin, Leman Feng, Mathieu Desbrun, Max Budninskiy, Yiying Tong","submitted_at":"2018-06-23T21:29:50Z","abstract_excerpt":"Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a quasi-isometric, low-dimensional mapping from a sparse and irregular sampling of an arbitrary manifold embedded in a high-dimensional space. Geodesic distances of discrete paths over the input pointset are evaluated through \"parallel transport unfolding\" (PTU) to offer robustness to poor sampling and arbitrary topology. Our new geometric procedure exhibits the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09039","kind":"arxiv","version":2},"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":"1806.09039","created_at":"2026-05-18T00:01:43.343001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09039v2","created_at":"2026-05-18T00:01:43.343001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09039","created_at":"2026-05-18T00:01:43.343001+00:00"},{"alias_kind":"pith_short_12","alias_value":"S243R3W4ZOE4","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"S243R3W4ZOE46K2E","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"S243R3W4","created_at":"2026-05-18T12:32:50.500415+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/S243R3W4ZOE46K2ED7UCUAEQYT","json":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT.json","graph_json":"https://pith.science/api/pith-number/S243R3W4ZOE46K2ED7UCUAEQYT/graph.json","events_json":"https://pith.science/api/pith-number/S243R3W4ZOE46K2ED7UCUAEQYT/events.json","paper":"https://pith.science/paper/S243R3W4"},"agent_actions":{"view_html":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT","download_json":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT.json","view_paper":"https://pith.science/paper/S243R3W4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09039&json=true","fetch_graph":"https://pith.science/api/pith-number/S243R3W4ZOE46K2ED7UCUAEQYT/graph.json","fetch_events":"https://pith.science/api/pith-number/S243R3W4ZOE46K2ED7UCUAEQYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT/action/storage_attestation","attest_author":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT/action/author_attestation","sign_citation":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT/action/citation_signature","submit_replication":"https://pith.science/pith/S243R3W4ZOE46K2ED7UCUAEQYT/action/replication_record"}},"created_at":"2026-05-18T00:01:43.343001+00:00","updated_at":"2026-05-18T00:01:43.343001+00:00"}