{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZBFTN4PMUC3QZOVJTEJK34JV2K","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"50bedcd023d13de86567a43e6cb96ba47d2e53979f250babc5edadd651f9cdb1","cross_cats_sorted":["cs.DM","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T21:49:48Z","title_canon_sha256":"b0e8e926e7d8101f5a69b2efcacbf8d26acc78c2b6e803c4d3d17aedaedfdf2e"},"schema_version":"1.0","source":{"id":"1710.11253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11253","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11253v2","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11253","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZBFTN4PMUC3Q","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZBFTN4PMUC3QZOVJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZBFTN4PM","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:d418f84cdca213e3c5d64987e78639eacd8838461dce31f9a22d115b0c436422","target":"graph","created_at":"2026-05-18T00:04:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the $\\ell_0$-Low Rank Approximation Problem, where the goal is, given an $m \\times n$ matrix $A$, to output a rank-$k$ matrix $A'$ for which $\\|A'-A\\|_0$ is minimized. Here, for a matrix $B$, $\\|B\\|_0$ denotes the number of its non-zero entries. This NP-hard variant of low rank approximation is natural for problems with no underlying metric, and its goal is to minimize the number of disagreeing data positions. We provide approximation algorithms which significantly improve the running time and approximation factor of previous work. For $k > 1$, we show how to find, in poly$(mn)$ time ","authors_text":"David P. Woodruff, Karl Bringmann, Pavel Kolev","cross_cats":["cs.DM","cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T21:49:48Z","title":"Approximation Algorithms for $\\ell_0$-Low Rank Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11253","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:06fc2b6831d2dbdb877eea1d44371e010f0ad398a582c14e7ec835590842784b","target":"record","created_at":"2026-05-18T00:04:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"50bedcd023d13de86567a43e6cb96ba47d2e53979f250babc5edadd651f9cdb1","cross_cats_sorted":["cs.DM","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T21:49:48Z","title_canon_sha256":"b0e8e926e7d8101f5a69b2efcacbf8d26acc78c2b6e803c4d3d17aedaedfdf2e"},"schema_version":"1.0","source":{"id":"1710.11253","kind":"arxiv","version":2}},"canonical_sha256":"c84b36f1eca0b70cbaa99912adf135d2972c90278d05cbc97f6d8a38185f1b31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c84b36f1eca0b70cbaa99912adf135d2972c90278d05cbc97f6d8a38185f1b31","first_computed_at":"2026-05-18T00:04:30.569194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:30.569194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7RPkzGM0ICKS99Cp2h08A78cblUkr2Gq8T9C4DJWFL+t2TFIyIG29uUuRbKLNNfJ6d7OiYYkgRkMrFajCiWzBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:30.569613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06fc2b6831d2dbdb877eea1d44371e010f0ad398a582c14e7ec835590842784b","sha256:d418f84cdca213e3c5d64987e78639eacd8838461dce31f9a22d115b0c436422"],"state_sha256":"df96de1d5b84eade3fbfc10d7327d65e27c6cd9dfd3b2f10f739e53275f6535d"}