{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DUDLCJCEZ36ETUKJ5DNBBXY6WC","short_pith_number":"pith:DUDLCJCE","canonical_record":{"source":{"id":"1503.08395","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-29T07:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"7a3940175a687647db9780dd36d907029dd4cf13d69f3e7ddb0c9b68b7288db9","abstract_canon_sha256":"96921f9aaf56d3846cbb9bd30df2ca4a77495966b4c2a94ad17c9539ce6a36e4"},"schema_version":"1.0"},"canonical_sha256":"1d06b12444cefc49d149e8da10df1eb08f6e24450e27a63bd903b8a3a9e788e9","source":{"kind":"arxiv","id":"1503.08395","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08395","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08395v6","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08395","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"DUDLCJCEZ36E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DUDLCJCEZ36ETUKJ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DUDLCJCE","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DUDLCJCEZ36ETUKJ5DNBBXY6WC","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08395","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-29T07:25:32Z","cross_cats_sorted":[],"title_canon_sha256":"7a3940175a687647db9780dd36d907029dd4cf13d69f3e7ddb0c9b68b7288db9","abstract_canon_sha256":"96921f9aaf56d3846cbb9bd30df2ca4a77495966b4c2a94ad17c9539ce6a36e4"},"schema_version":"1.0"},"canonical_sha256":"1d06b12444cefc49d149e8da10df1eb08f6e24450e27a63bd903b8a3a9e788e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:25.797137Z","signature_b64":"6z5GwL4xu8vtcPungx3K+oc0Y7IzmNxLXpgMTWB71YQFTNzwsFLiA3J2Bx42WMC356a7xXABsOK5XwHsgJatCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d06b12444cefc49d149e8da10df1eb08f6e24450e27a63bd903b8a3a9e788e9","last_reissued_at":"2026-05-18T00:55:25.796647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:25.796647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08395","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYIY+ybMidRo/8MPho3U6f0CKNRMhuhpurFJvbwxOc9i2NNEnDw6H0/PyP+ZjFvOXOiiCpczh+NWWgbfxeATBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:30:43.480780Z"},"content_sha256":"23a13004b8aea7e71a47c2d2c3de0fc538cad4c9d527e119667b471f80d70288","schema_version":"1.0","event_id":"sha256:23a13004b8aea7e71a47c2d2c3de0fc538cad4c9d527e119667b471f80d70288"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DUDLCJCEZ36ETUKJ5DNBBXY6WC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards More Efficient SPSD Matrix Approximation and CUR Matrix Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Shusen Wang, Tong Zhang, Zhihua Zhang","submitted_at":"2015-03-29T07:25:32Z","abstract_excerpt":"Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but is inefficient on large square matrices. The Nystr\\\"om method is highly efficient, but can only achieve low accuracy. In this paper we propose a novel model that we call the {\\it fast SPSD matrix approximation model}. The fast model is nearly as efficient as the Nystr\\\"om method and as accurate as the prototy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08395","kind":"arxiv","version":6},"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":"2026-05-18T00:55:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDz23UaZlViYq0MWtna4dp6t1Lt0lH2q1fyiGYUkLGwjz3gdNmuLRUt1owBnqJLy23d5yTTTjOHjc8MG696LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:30:43.481513Z"},"content_sha256":"4538f6ecf3a1213997b9467212f310519f12eae17b6d8ba66c3015fa03e5d64a","schema_version":"1.0","event_id":"sha256:4538f6ecf3a1213997b9467212f310519f12eae17b6d8ba66c3015fa03e5d64a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/bundle.json","state_url":"https://pith.science/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/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":"2026-05-30T01:30:43Z","links":{"resolver":"https://pith.science/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC","bundle":"https://pith.science/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/bundle.json","state":"https://pith.science/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUDLCJCEZ36ETUKJ5DNBBXY6WC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DUDLCJCEZ36ETUKJ5DNBBXY6WC","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":"96921f9aaf56d3846cbb9bd30df2ca4a77495966b4c2a94ad17c9539ce6a36e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-29T07:25:32Z","title_canon_sha256":"7a3940175a687647db9780dd36d907029dd4cf13d69f3e7ddb0c9b68b7288db9"},"schema_version":"1.0","source":{"id":"1503.08395","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08395","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08395v6","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08395","created_at":"2026-05-18T00:55:25Z"},{"alias_kind":"pith_short_12","alias_value":"DUDLCJCEZ36E","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DUDLCJCEZ36ETUKJ","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DUDLCJCE","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:4538f6ecf3a1213997b9467212f310519f12eae17b6d8ba66c3015fa03e5d64a","target":"graph","created_at":"2026-05-18T00:55:25Z","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":"Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but is inefficient on large square matrices. The Nystr\\\"om method is highly efficient, but can only achieve low accuracy. In this paper we propose a novel model that we call the {\\it fast SPSD matrix approximation model}. The fast model is nearly as efficient as the Nystr\\\"om method and as accurate as the prototy","authors_text":"Shusen Wang, Tong Zhang, Zhihua Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-29T07:25:32Z","title":"Towards More Efficient SPSD Matrix Approximation and CUR Matrix Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08395","kind":"arxiv","version":6},"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":"sha256:23a13004b8aea7e71a47c2d2c3de0fc538cad4c9d527e119667b471f80d70288","target":"record","created_at":"2026-05-18T00:55:25Z","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":"96921f9aaf56d3846cbb9bd30df2ca4a77495966b4c2a94ad17c9539ce6a36e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-29T07:25:32Z","title_canon_sha256":"7a3940175a687647db9780dd36d907029dd4cf13d69f3e7ddb0c9b68b7288db9"},"schema_version":"1.0","source":{"id":"1503.08395","kind":"arxiv","version":6}},"canonical_sha256":"1d06b12444cefc49d149e8da10df1eb08f6e24450e27a63bd903b8a3a9e788e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d06b12444cefc49d149e8da10df1eb08f6e24450e27a63bd903b8a3a9e788e9","first_computed_at":"2026-05-18T00:55:25.796647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:25.796647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6z5GwL4xu8vtcPungx3K+oc0Y7IzmNxLXpgMTWB71YQFTNzwsFLiA3J2Bx42WMC356a7xXABsOK5XwHsgJatCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:25.797137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08395","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23a13004b8aea7e71a47c2d2c3de0fc538cad4c9d527e119667b471f80d70288","sha256:4538f6ecf3a1213997b9467212f310519f12eae17b6d8ba66c3015fa03e5d64a"],"state_sha256":"4b32d20c48c7d4132a0f2288c61169f7165c03188fce58bf463322d2d4cecb29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YA8eSwk0MH8sLCxgWonYT9zDgODIoUSz8+HaVFB/BmFPcdElOHByVWadhi7BYsYKfGQJYcT2StIJTYNH+ViJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:30:43.484782Z","bundle_sha256":"344a92a7b2849d89585416140571fd6a6f7c039e95b07fcd9f0fcc3897b2789d"}}