{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HM7PNV3WL75L36VPHG3HE4GFFN","short_pith_number":"pith:HM7PNV3W","schema_version":"1.0","canonical_sha256":"3b3ef6d7765ffabdfaaf39b67270c52b6d1dc4d99819e165111b888b83bb06cb","source":{"kind":"arxiv","id":"1405.6785","version":1},"attestation_state":"computed","paper":{"title":"Optimal Algorithms for $L_1$-subspace Signal Processing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dimitris A. Pados, George N. Karystinos, Panos P. Markopoulos","submitted_at":"2014-05-27T04:15:49Z","abstract_excerpt":"We describe ways to define and calculate $L_1$-norm signal subspaces which are less sensitive to outlying data than $L_2$-calculated subspaces. We start with the computation of the $L_1$ maximum-projection principal component of a data matrix containing $N$ signal samples of dimension $D$. We show that while the general problem is formally NP-hard in asymptotically large $N$, $D$, the case of engineering interest of fixed dimension $D$ and asymptotically large sample size $N$ is not. In particular, for the case where the sample size is less than the fixed dimension ($N<D$), we present in expli"},"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":"1405.6785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-27T04:15:49Z","cross_cats_sorted":[],"title_canon_sha256":"6528fc2b1a0f4f1a57660336e4d92be6a2e350e77a33d4eac62499deab076017","abstract_canon_sha256":"b6fa3462eb33725f3bd4e3bd2678963b9b12d710630208011a4d191c069bd1ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:05.972025Z","signature_b64":"VEW04TxDEcMhDcMQmXBOQgoBK5oJG2XO/Qhr5GEV2oszaTc75a6kOLBVnC6rkgW+VU9Uo6aCCjt+5OOZE2xiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b3ef6d7765ffabdfaaf39b67270c52b6d1dc4d99819e165111b888b83bb06cb","last_reissued_at":"2026-05-18T01:43:05.971440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:05.971440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Algorithms for $L_1$-subspace Signal Processing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dimitris A. Pados, George N. Karystinos, Panos P. Markopoulos","submitted_at":"2014-05-27T04:15:49Z","abstract_excerpt":"We describe ways to define and calculate $L_1$-norm signal subspaces which are less sensitive to outlying data than $L_2$-calculated subspaces. We start with the computation of the $L_1$ maximum-projection principal component of a data matrix containing $N$ signal samples of dimension $D$. We show that while the general problem is formally NP-hard in asymptotically large $N$, $D$, the case of engineering interest of fixed dimension $D$ and asymptotically large sample size $N$ is not. In particular, for the case where the sample size is less than the fixed dimension ($N<D$), we present in expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6785","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":"1405.6785","created_at":"2026-05-18T01:43:05.971525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.6785v1","created_at":"2026-05-18T01:43:05.971525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6785","created_at":"2026-05-18T01:43:05.971525+00:00"},{"alias_kind":"pith_short_12","alias_value":"HM7PNV3WL75L","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HM7PNV3WL75L36VP","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HM7PNV3W","created_at":"2026-05-18T12:28:30.664211+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/HM7PNV3WL75L36VPHG3HE4GFFN","json":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN.json","graph_json":"https://pith.science/api/pith-number/HM7PNV3WL75L36VPHG3HE4GFFN/graph.json","events_json":"https://pith.science/api/pith-number/HM7PNV3WL75L36VPHG3HE4GFFN/events.json","paper":"https://pith.science/paper/HM7PNV3W"},"agent_actions":{"view_html":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN","download_json":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN.json","view_paper":"https://pith.science/paper/HM7PNV3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.6785&json=true","fetch_graph":"https://pith.science/api/pith-number/HM7PNV3WL75L36VPHG3HE4GFFN/graph.json","fetch_events":"https://pith.science/api/pith-number/HM7PNV3WL75L36VPHG3HE4GFFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN/action/storage_attestation","attest_author":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN/action/author_attestation","sign_citation":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN/action/citation_signature","submit_replication":"https://pith.science/pith/HM7PNV3WL75L36VPHG3HE4GFFN/action/replication_record"}},"created_at":"2026-05-18T01:43:05.971525+00:00","updated_at":"2026-05-18T01:43:05.971525+00:00"}