{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:46XSUHRDPSKRU3PSB4KO4XH25W","short_pith_number":"pith:46XSUHRD","canonical_record":{"source":{"id":"1210.1461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-04T14:23:34Z","cross_cats_sorted":["cs.DM","stat.ML"],"title_canon_sha256":"f4f0789a45fd75290baaaea245bc1423986a7aaaf43ba5ec224efa7bf4417dc0","abstract_canon_sha256":"db33006b12ca2cdb8114a586275e602ee10ca1906ffabc2fd388d413a42f4a27"},"schema_version":"1.0"},"canonical_sha256":"e7af2a1e237c951a6df20f14ee5cfaed8563611f6422f4f2b40d52d9bae8fce8","source":{"kind":"arxiv","id":"1210.1461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1461","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1461v1","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1461","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"pith_short_12","alias_value":"46XSUHRDPSKR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"46XSUHRDPSKRU3PS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"46XSUHRD","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:46XSUHRDPSKRU3PSB4KO4XH25W","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-04T14:23:34Z","cross_cats_sorted":["cs.DM","stat.ML"],"title_canon_sha256":"f4f0789a45fd75290baaaea245bc1423986a7aaaf43ba5ec224efa7bf4417dc0","abstract_canon_sha256":"db33006b12ca2cdb8114a586275e602ee10ca1906ffabc2fd388d413a42f4a27"},"schema_version":"1.0"},"canonical_sha256":"e7af2a1e237c951a6df20f14ee5cfaed8563611f6422f4f2b40d52d9bae8fce8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:03.471407Z","signature_b64":"P3tKfkiqNyqxc84FZJ8IkZHqR7zEUZjdjNG5z08y/QrlhosItajcOXddXzv/BfUtFccQX+s6NsFVhevRhUzVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7af2a1e237c951a6df20f14ee5cfaed8563611f6422f4f2b40d52d9bae8fce8","last_reissued_at":"2026-05-18T03:44:03.470627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:03.470627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1461","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZM2/rCeXrAEYebMxhLq4RCIEMvTSS6+78/EpbNZhtOQrHxE00veXsSkZTM6kQ2i69gzqAysNsWm4ZM0mBsr6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:59:25.720821Z"},"content_sha256":"369a4ade33d385f92181edf0107788b6fe4b823418a0fc6edd068bdb10f7204c","schema_version":"1.0","event_id":"sha256:369a4ade33d385f92181edf0107788b6fe4b823418a0fc6edd068bdb10f7204c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:46XSUHRDPSKRU3PSB4KO4XH25W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Scalable CUR Matrix Decomposition Algorithm: Lower Time Complexity and Tighter Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","stat.ML"],"primary_cat":"cs.LG","authors_text":"Jian Li, Shusen Wang, Zhihua Zhang","submitted_at":"2012-10-04T14:23:34Z","abstract_excerpt":"The CUR matrix decomposition is an important extension of Nystr\\\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter theoretical bound and lower time complexity, and that it can avoid maintaining the whole data matrix in main memory. Finally, experiments on several real-world datasets demonstrate significant impro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1461","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3C/NFfIbyNnEzeOQKJJMoz/POM7GuPVO3ppS64Cj3Y/ejGb0QGFlMwI5AlCzglVH7mg5kYjKvhRvYeTnuK0FCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:59:25.721474Z"},"content_sha256":"31e343ffb465e781ac814c7d1a442aeb10a9c7da5ac6f1babd9b4860a59db3d8","schema_version":"1.0","event_id":"sha256:31e343ffb465e781ac814c7d1a442aeb10a9c7da5ac6f1babd9b4860a59db3d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46XSUHRDPSKRU3PSB4KO4XH25W/bundle.json","state_url":"https://pith.science/pith/46XSUHRDPSKRU3PSB4KO4XH25W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46XSUHRDPSKRU3PSB4KO4XH25W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T18:59:25Z","links":{"resolver":"https://pith.science/pith/46XSUHRDPSKRU3PSB4KO4XH25W","bundle":"https://pith.science/pith/46XSUHRDPSKRU3PSB4KO4XH25W/bundle.json","state":"https://pith.science/pith/46XSUHRDPSKRU3PSB4KO4XH25W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46XSUHRDPSKRU3PSB4KO4XH25W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:46XSUHRDPSKRU3PSB4KO4XH25W","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":"db33006b12ca2cdb8114a586275e602ee10ca1906ffabc2fd388d413a42f4a27","cross_cats_sorted":["cs.DM","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-04T14:23:34Z","title_canon_sha256":"f4f0789a45fd75290baaaea245bc1423986a7aaaf43ba5ec224efa7bf4417dc0"},"schema_version":"1.0","source":{"id":"1210.1461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1461","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1461v1","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1461","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"pith_short_12","alias_value":"46XSUHRDPSKR","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"46XSUHRDPSKRU3PS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"46XSUHRD","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:31e343ffb465e781ac814c7d1a442aeb10a9c7da5ac6f1babd9b4860a59db3d8","target":"graph","created_at":"2026-05-18T03:44:03Z","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":"The CUR matrix decomposition is an important extension of Nystr\\\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advantages over the existing relative-error CUR algorithms that it possesses tighter theoretical bound and lower time complexity, and that it can avoid maintaining the whole data matrix in main memory. Finally, experiments on several real-world datasets demonstrate significant impro","authors_text":"Jian Li, Shusen Wang, Zhihua Zhang","cross_cats":["cs.DM","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-04T14:23:34Z","title":"A Scalable CUR Matrix Decomposition Algorithm: Lower Time Complexity and Tighter Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1461","kind":"arxiv","version":1},"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":"sha256:369a4ade33d385f92181edf0107788b6fe4b823418a0fc6edd068bdb10f7204c","target":"record","created_at":"2026-05-18T03:44:03Z","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":"db33006b12ca2cdb8114a586275e602ee10ca1906ffabc2fd388d413a42f4a27","cross_cats_sorted":["cs.DM","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-10-04T14:23:34Z","title_canon_sha256":"f4f0789a45fd75290baaaea245bc1423986a7aaaf43ba5ec224efa7bf4417dc0"},"schema_version":"1.0","source":{"id":"1210.1461","kind":"arxiv","version":1}},"canonical_sha256":"e7af2a1e237c951a6df20f14ee5cfaed8563611f6422f4f2b40d52d9bae8fce8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7af2a1e237c951a6df20f14ee5cfaed8563611f6422f4f2b40d52d9bae8fce8","first_computed_at":"2026-05-18T03:44:03.470627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:03.470627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P3tKfkiqNyqxc84FZJ8IkZHqR7zEUZjdjNG5z08y/QrlhosItajcOXddXzv/BfUtFccQX+s6NsFVhevRhUzVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:03.471407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:369a4ade33d385f92181edf0107788b6fe4b823418a0fc6edd068bdb10f7204c","sha256:31e343ffb465e781ac814c7d1a442aeb10a9c7da5ac6f1babd9b4860a59db3d8"],"state_sha256":"fdfa0a3963485cfc9bea5a60888aa9cc59bb39e928227b93b6932f242e6aa46b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wj/8b5BtlycC5Jf50MUUyxm+j9gR1tKh4A8ExWQQM79TtV0ajnMslJpzucJWmintsD9m8l1jEF0+9/tSuSiBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:59:25.725403Z","bundle_sha256":"f482c0ebe61ba502c8b52e1477a1b5a0707fddb606515ea4e6aff91cc45ebc56"}}