{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AOZAERUD54FYVZQJT43SUWICOZ","short_pith_number":"pith:AOZAERUD","schema_version":"1.0","canonical_sha256":"03b2024683ef0b8ae6099f372a590276796fb05b492070e2551eda8cc19779a1","source":{"kind":"arxiv","id":"1412.6752","version":1},"attestation_state":"computed","paper":{"title":"Correlation of Data Reconstruction Error and Shrinkages in Pair-wise Distances under Principal Component Analysis (PCA)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Abdulrahman Oladipupo Ibraheem","submitted_at":"2014-12-21T09:50:32Z","abstract_excerpt":"In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are discarded 2). PCA without discarding eigen- vector rows preserves pair-wise distances, but tends to cause pair-wise distances to shrink when eigenvector rows are discarded. 3). For any pair of points, the shrinkage in pair-wise distance is bounded above by an L1 norm reconstruct"},"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":"1412.6752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-21T09:50:32Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a1ad2ae61d417a6e28cadfb4dba599422c811073ac408b3238c751ef56cbad38","abstract_canon_sha256":"dec3e44c2da5d7abab469b9bf5d3a674333837778b6f7db30ebdd2c1da9f9178"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:46.299513Z","signature_b64":"vY4pRs1u6V4hzzlDdYhk2BQy1a/Cr2tIhW1DbXlSWmDbsZEH3anFYoSUD7GJ+DFBYLmw64zEfWeCGjKhNwriCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03b2024683ef0b8ae6099f372a590276796fb05b492070e2551eda8cc19779a1","last_reissued_at":"2026-05-18T02:30:46.299107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:46.299107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlation of Data Reconstruction Error and Shrinkages in Pair-wise Distances under Principal Component Analysis (PCA)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Abdulrahman Oladipupo Ibraheem","submitted_at":"2014-12-21T09:50:32Z","abstract_excerpt":"In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are discarded 2). PCA without discarding eigen- vector rows preserves pair-wise distances, but tends to cause pair-wise distances to shrink when eigenvector rows are discarded. 3). For any pair of points, the shrinkage in pair-wise distance is bounded above by an L1 norm reconstruct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6752","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":"1412.6752","created_at":"2026-05-18T02:30:46.299170+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.6752v1","created_at":"2026-05-18T02:30:46.299170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6752","created_at":"2026-05-18T02:30:46.299170+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOZAERUD54FY","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOZAERUD54FYVZQJ","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOZAERUD","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.14941","citing_title":"nASR: An End-to-End Trainable Neural Layer for Channel-Level EEG Artifact Subspace Reconstruction in Real-Time BCI","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ","json":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ.json","graph_json":"https://pith.science/api/pith-number/AOZAERUD54FYVZQJT43SUWICOZ/graph.json","events_json":"https://pith.science/api/pith-number/AOZAERUD54FYVZQJT43SUWICOZ/events.json","paper":"https://pith.science/paper/AOZAERUD"},"agent_actions":{"view_html":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ","download_json":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ.json","view_paper":"https://pith.science/paper/AOZAERUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.6752&json=true","fetch_graph":"https://pith.science/api/pith-number/AOZAERUD54FYVZQJT43SUWICOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AOZAERUD54FYVZQJT43SUWICOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ/action/storage_attestation","attest_author":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ/action/author_attestation","sign_citation":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ/action/citation_signature","submit_replication":"https://pith.science/pith/AOZAERUD54FYVZQJT43SUWICOZ/action/replication_record"}},"created_at":"2026-05-18T02:30:46.299170+00:00","updated_at":"2026-05-18T02:30:46.299170+00:00"}