{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EQYIWNXZE6X227DVGKEZWMDSLQ","short_pith_number":"pith:EQYIWNXZ","schema_version":"1.0","canonical_sha256":"24308b36f927afad7c7532899b30725c2eeb213a2a067ec3d5f9b4e63d12dc2c","source":{"kind":"arxiv","id":"1811.00115","version":1},"attestation_state":"computed","paper":{"title":"Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Gavin Weiguang Ding, Kry Yik Chau Lui, Robert J. McCann, Ruitong Huang","submitted_at":"2018-10-31T20:56:14Z","abstract_excerpt":"In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall simultaneously. Thus a continuous DR map must have imperfect precision. We further prove an upper bound on the precision of Lipschitz continuous DR maps. While precision is a natural measure in an information retrieval setting, it does not measure `how' wrong the retrieved data is. We therefore propose a new measure based on Wasserstein distance that comes with sim"},"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":"1811.00115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-10-31T20:56:14Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a7ddecd8d0b68372633a6881046000f7d1fbd39e2be93e62d3a430eed80d8849","abstract_canon_sha256":"d880c02fc26a1231692409a1a985cdbc46bf975344630df4593e3f512cd99afa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.215973Z","signature_b64":"SWjqUnMUDc/ETSKClgNYVPlEq6X4toVtHz3p5TJnbh0BR86+rjgipvss7Dbl2JFXesMZ7KpPS59egxXFVAdQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24308b36f927afad7c7532899b30725c2eeb213a2a067ec3d5f9b4e63d12dc2c","last_reissued_at":"2026-05-18T00:01:48.215408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.215408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimensionality Reduction has Quantifiable Imperfections: Two Geometric Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Gavin Weiguang Ding, Kry Yik Chau Lui, Robert J. McCann, Ruitong Huang","submitted_at":"2018-10-31T20:56:14Z","abstract_excerpt":"In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall simultaneously. Thus a continuous DR map must have imperfect precision. We further prove an upper bound on the precision of Lipschitz continuous DR maps. While precision is a natural measure in an information retrieval setting, it does not measure `how' wrong the retrieved data is. We therefore propose a new measure based on Wasserstein distance that comes with sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00115","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":"1811.00115","created_at":"2026-05-18T00:01:48.215495+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00115v1","created_at":"2026-05-18T00:01:48.215495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00115","created_at":"2026-05-18T00:01:48.215495+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQYIWNXZE6X2","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQYIWNXZE6X227DV","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQYIWNXZ","created_at":"2026-05-18T12:32:22.470017+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/EQYIWNXZE6X227DVGKEZWMDSLQ","json":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ.json","graph_json":"https://pith.science/api/pith-number/EQYIWNXZE6X227DVGKEZWMDSLQ/graph.json","events_json":"https://pith.science/api/pith-number/EQYIWNXZE6X227DVGKEZWMDSLQ/events.json","paper":"https://pith.science/paper/EQYIWNXZ"},"agent_actions":{"view_html":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ","download_json":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ.json","view_paper":"https://pith.science/paper/EQYIWNXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00115&json=true","fetch_graph":"https://pith.science/api/pith-number/EQYIWNXZE6X227DVGKEZWMDSLQ/graph.json","fetch_events":"https://pith.science/api/pith-number/EQYIWNXZE6X227DVGKEZWMDSLQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ/action/storage_attestation","attest_author":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ/action/author_attestation","sign_citation":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ/action/citation_signature","submit_replication":"https://pith.science/pith/EQYIWNXZE6X227DVGKEZWMDSLQ/action/replication_record"}},"created_at":"2026-05-18T00:01:48.215495+00:00","updated_at":"2026-05-18T00:01:48.215495+00:00"}