{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3FPJ3GA2AQGTAXEPG3KAXQTWOL","short_pith_number":"pith:3FPJ3GA2","schema_version":"1.0","canonical_sha256":"d95e9d981a040d305c8f36d40bc27672f569c8682e0c78690dea60238010f4cb","source":{"kind":"arxiv","id":"2501.13732","version":2},"attestation_state":"computed","paper":{"title":"A dimensionality reduction technique based on the Gromov-Wasserstein distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Charles C. Cavalcante, Eduardo Fernandes Montesuma, Rafael P. Eufrazio","submitted_at":"2025-01-23T15:05:51Z","abstract_excerpt":"Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we "},"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":"2501.13732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-01-23T15:05:51Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b63b3b50e486d165a92e2d05ba4885611c89403db50f84ef99a156b88749f813","abstract_canon_sha256":"9b7b5eb9807b050dff5d0441cc86245a61532f02f2b63558c3aca9214de80d20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:03.498745Z","signature_b64":"HC7gcS68ekyQ71bIDqorHjIiK7kXz6oplhkSQAmLBjJdVf6jt98b6TWs1G7dQ+NE78aaMKmP/ojb7ASd99l5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d95e9d981a040d305c8f36d40bc27672f569c8682e0c78690dea60238010f4cb","last_reissued_at":"2026-07-05T11:33:03.498222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:03.498222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A dimensionality reduction technique based on the Gromov-Wasserstein distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Charles C. Cavalcante, Eduardo Fernandes Montesuma, Rafael P. Eufrazio","submitted_at":"2025-01-23T15:05:51Z","abstract_excerpt":"Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13732","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.13732/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2501.13732","created_at":"2026-07-05T11:33:03.498288+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.13732v2","created_at":"2026-07-05T11:33:03.498288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13732","created_at":"2026-07-05T11:33:03.498288+00:00"},{"alias_kind":"pith_short_12","alias_value":"3FPJ3GA2AQGT","created_at":"2026-07-05T11:33:03.498288+00:00"},{"alias_kind":"pith_short_16","alias_value":"3FPJ3GA2AQGTAXEP","created_at":"2026-07-05T11:33:03.498288+00:00"},{"alias_kind":"pith_short_8","alias_value":"3FPJ3GA2","created_at":"2026-07-05T11:33:03.498288+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/3FPJ3GA2AQGTAXEPG3KAXQTWOL","json":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL.json","graph_json":"https://pith.science/api/pith-number/3FPJ3GA2AQGTAXEPG3KAXQTWOL/graph.json","events_json":"https://pith.science/api/pith-number/3FPJ3GA2AQGTAXEPG3KAXQTWOL/events.json","paper":"https://pith.science/paper/3FPJ3GA2"},"agent_actions":{"view_html":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL","download_json":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL.json","view_paper":"https://pith.science/paper/3FPJ3GA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.13732&json=true","fetch_graph":"https://pith.science/api/pith-number/3FPJ3GA2AQGTAXEPG3KAXQTWOL/graph.json","fetch_events":"https://pith.science/api/pith-number/3FPJ3GA2AQGTAXEPG3KAXQTWOL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL/action/storage_attestation","attest_author":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL/action/author_attestation","sign_citation":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL/action/citation_signature","submit_replication":"https://pith.science/pith/3FPJ3GA2AQGTAXEPG3KAXQTWOL/action/replication_record"}},"created_at":"2026-07-05T11:33:03.498288+00:00","updated_at":"2026-07-05T11:33:03.498288+00:00"}