{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KI6GBYDL54Q5AZI7KJ7EAHENDT","short_pith_number":"pith:KI6GBYDL","schema_version":"1.0","canonical_sha256":"523c60e06bef21d0651f527e401c8d1cf62a5e7630464123258dc644690ed1e8","source":{"kind":"arxiv","id":"1610.01959","version":1},"attestation_state":"computed","paper":{"title":"Efficient L1-Norm Principal-Component Analysis via Bit Flipping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Dimitris A. Pados, Panos P. Markopoulos, Sandipan Kundu, Shubham Chamadia","submitted_at":"2016-10-06T17:20:16Z","abstract_excerpt":"It was shown recently that the $K$ L1-norm principal components (L1-PCs) of a real-valued data matrix $\\mathbf X \\in \\mathbb R^{D \\times N}$ ($N$ data samples of $D$ dimensions) can be exactly calculated with cost $\\mathcal{O}(2^{NK})$ or, when advantageous, $\\mathcal{O}(N^{dK - K + 1})$ where $d=\\mathrm{rank}(\\mathbf X)$, $K<d$ [1],[2]. In applications where $\\mathbf X$ is large (e.g., \"big\" data of large $N$ and/or \"heavy\" data of large $d$), these costs are prohibitive. In this work, we present a novel suboptimal algorithm for the calculation of the $K < d$ L1-PCs of $\\mathbf X$ of cost $\\m"},"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":"1610.01959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-06T17:20:16Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"57cb8446d5ae257eed341735387f369d81b6161a4769f9416bc374c3eeecbe29","abstract_canon_sha256":"472c18079b9cd86f3fae3839883f1df37ada66982b76554a44ac0d2fa86d8909"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:01.858198Z","signature_b64":"EbvIg7tZ814QZjVD1tG4/8bGCqUGNBtOL/ysafNliSynt4Yc4RPO/K1AvClu5iDoaC3e0jUEHbYQcGVY6+z7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"523c60e06bef21d0651f527e401c8d1cf62a5e7630464123258dc644690ed1e8","last_reissued_at":"2026-05-18T00:39:01.857579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:01.857579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient L1-Norm Principal-Component Analysis via Bit Flipping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Dimitris A. Pados, Panos P. Markopoulos, Sandipan Kundu, Shubham Chamadia","submitted_at":"2016-10-06T17:20:16Z","abstract_excerpt":"It was shown recently that the $K$ L1-norm principal components (L1-PCs) of a real-valued data matrix $\\mathbf X \\in \\mathbb R^{D \\times N}$ ($N$ data samples of $D$ dimensions) can be exactly calculated with cost $\\mathcal{O}(2^{NK})$ or, when advantageous, $\\mathcal{O}(N^{dK - K + 1})$ where $d=\\mathrm{rank}(\\mathbf X)$, $K<d$ [1],[2]. In applications where $\\mathbf X$ is large (e.g., \"big\" data of large $N$ and/or \"heavy\" data of large $d$), these costs are prohibitive. In this work, we present a novel suboptimal algorithm for the calculation of the $K < d$ L1-PCs of $\\mathbf X$ of cost $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01959","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":"1610.01959","created_at":"2026-05-18T00:39:01.857671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.01959v1","created_at":"2026-05-18T00:39:01.857671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01959","created_at":"2026-05-18T00:39:01.857671+00:00"},{"alias_kind":"pith_short_12","alias_value":"KI6GBYDL54Q5","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KI6GBYDL54Q5AZI7","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KI6GBYDL","created_at":"2026-05-18T12:30:25.849896+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/KI6GBYDL54Q5AZI7KJ7EAHENDT","json":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT.json","graph_json":"https://pith.science/api/pith-number/KI6GBYDL54Q5AZI7KJ7EAHENDT/graph.json","events_json":"https://pith.science/api/pith-number/KI6GBYDL54Q5AZI7KJ7EAHENDT/events.json","paper":"https://pith.science/paper/KI6GBYDL"},"agent_actions":{"view_html":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT","download_json":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT.json","view_paper":"https://pith.science/paper/KI6GBYDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.01959&json=true","fetch_graph":"https://pith.science/api/pith-number/KI6GBYDL54Q5AZI7KJ7EAHENDT/graph.json","fetch_events":"https://pith.science/api/pith-number/KI6GBYDL54Q5AZI7KJ7EAHENDT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT/action/storage_attestation","attest_author":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT/action/author_attestation","sign_citation":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT/action/citation_signature","submit_replication":"https://pith.science/pith/KI6GBYDL54Q5AZI7KJ7EAHENDT/action/replication_record"}},"created_at":"2026-05-18T00:39:01.857671+00:00","updated_at":"2026-05-18T00:39:01.857671+00:00"}