{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:IELRGIIXFCJLZFNYKRRPVNZTJU","short_pith_number":"pith:IELRGIIX","schema_version":"1.0","canonical_sha256":"41171321172892bc95b85462fab7334d26afb4cf2ac3e73aeb578996245a8bfb","source":{"kind":"arxiv","id":"2011.13476","version":1},"attestation_state":"computed","paper":{"title":"Faster Projective Clustering Approximation of Big Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adiel Statman, Dan Feldman, Liat Rozenberg","submitted_at":"2020-11-26T21:04:41Z","abstract_excerpt":"In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\\eps$-coreset for this problem is a weighted (scaled) subset of the input points such that for every such possible $S$ the sum of these distances is approximated up to a factor of $(1+\\eps)$. We suggest to reduce the size of existing coresets by suggesting the first $O(\\log(m))$ approximation for the case of $m$ lines clustering in $O(ndm)$ time, compared to the existing $\\exp(m)$ solution. We then project the poi"},"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":"2011.13476","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-26T21:04:41Z","cross_cats_sorted":[],"title_canon_sha256":"d22760b0ddde969e9633ad23ee65efb5ce88ca5b77619c68f351fd2e3ecd77e0","abstract_canon_sha256":"ee7c570e25d3ec3493b34873503a15620cf75e3184db2fb84944d5c06927dfdd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:54:54.599440Z","signature_b64":"ooD/Mt1pF6B6oCYz2ub+CasFOks6ME9RA8pOGUeSPRfuUx6t8VXBvk/a6wd6FADFt4FimC8GVYdvllRWxoDbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41171321172892bc95b85462fab7334d26afb4cf2ac3e73aeb578996245a8bfb","last_reissued_at":"2026-07-05T01:54:54.599010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:54:54.599010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faster Projective Clustering Approximation of Big Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adiel Statman, Dan Feldman, Liat Rozenberg","submitted_at":"2020-11-26T21:04:41Z","abstract_excerpt":"In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\\eps$-coreset for this problem is a weighted (scaled) subset of the input points such that for every such possible $S$ the sum of these distances is approximated up to a factor of $(1+\\eps)$. We suggest to reduce the size of existing coresets by suggesting the first $O(\\log(m))$ approximation for the case of $m$ lines clustering in $O(ndm)$ time, compared to the existing $\\exp(m)$ solution. We then project the poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13476","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.13476/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":"2011.13476","created_at":"2026-07-05T01:54:54.599067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2011.13476v1","created_at":"2026-07-05T01:54:54.599067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.13476","created_at":"2026-07-05T01:54:54.599067+00:00"},{"alias_kind":"pith_short_12","alias_value":"IELRGIIXFCJL","created_at":"2026-07-05T01:54:54.599067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IELRGIIXFCJLZFNY","created_at":"2026-07-05T01:54:54.599067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IELRGIIX","created_at":"2026-07-05T01:54:54.599067+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/IELRGIIXFCJLZFNYKRRPVNZTJU","json":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU.json","graph_json":"https://pith.science/api/pith-number/IELRGIIXFCJLZFNYKRRPVNZTJU/graph.json","events_json":"https://pith.science/api/pith-number/IELRGIIXFCJLZFNYKRRPVNZTJU/events.json","paper":"https://pith.science/paper/IELRGIIX"},"agent_actions":{"view_html":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU","download_json":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU.json","view_paper":"https://pith.science/paper/IELRGIIX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2011.13476&json=true","fetch_graph":"https://pith.science/api/pith-number/IELRGIIXFCJLZFNYKRRPVNZTJU/graph.json","fetch_events":"https://pith.science/api/pith-number/IELRGIIXFCJLZFNYKRRPVNZTJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU/action/storage_attestation","attest_author":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU/action/author_attestation","sign_citation":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU/action/citation_signature","submit_replication":"https://pith.science/pith/IELRGIIXFCJLZFNYKRRPVNZTJU/action/replication_record"}},"created_at":"2026-07-05T01:54:54.599067+00:00","updated_at":"2026-07-05T01:54:54.599067+00:00"}