{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4AUFBBKBLFKC7S4KNVYCWXVPEC","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":"6a9a229df9418caba74057c14a73add7c55759a0a3fa578aa5ff978e8b4e02fd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-24T19:43:16Z","title_canon_sha256":"a13a656831f3a979ed248d4928591ebc5bcbc5302c7d1c6a3e08d01784db1425"},"schema_version":"1.0","source":{"id":"1410.6801","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6801","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6801v3","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6801","created_at":"2026-05-18T02:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"4AUFBBKBLFKC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4AUFBBKBLFKC7S4K","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4AUFBBKB","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:f6a48425c372a794a31f3e50d152f2ed22d97441fbe1e62bfb8be56c2de86b19","target":"graph","created_at":"2026-05-18T02:19:42Z","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 show how to approximate a data matrix $\\mathbf{A}$ with a much smaller sketch $\\mathbf{\\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\\epsilon)$ error. Importantly, this class of problems includes $k$-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just $O(k)$ dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems.\n  For $k$-means dimensionality reduction, we provide $(1+\\epsilon)$ rela","authors_text":"Cameron Musco, Christopher Musco, Madalina Persu, Michael B. Cohen, Sam Elder","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-24T19:43:16Z","title":"Dimensionality Reduction for k-Means Clustering and Low Rank Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6801","kind":"arxiv","version":3},"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":"sha256:42bdad7d2efabcb2dc84e5e001153ed59fad146dad66bbc8e3970b5f0ad2432e","target":"record","created_at":"2026-05-18T02:19:42Z","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":"6a9a229df9418caba74057c14a73add7c55759a0a3fa578aa5ff978e8b4e02fd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-24T19:43:16Z","title_canon_sha256":"a13a656831f3a979ed248d4928591ebc5bcbc5302c7d1c6a3e08d01784db1425"},"schema_version":"1.0","source":{"id":"1410.6801","kind":"arxiv","version":3}},"canonical_sha256":"e02850854159542fcb8a6d702b5eaf20850306314c2ca1eb70ae85667a9560e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e02850854159542fcb8a6d702b5eaf20850306314c2ca1eb70ae85667a9560e7","first_computed_at":"2026-05-18T02:19:42.502263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:42.502263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAUNdEmpl+PmkQnWovgBAM9XhIc/LxDHdymsJ92Bs188wAknbcG00Bx0LNjpGKK4hE5us1xDqVkP8+l7f+wQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:42.502734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6801","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42bdad7d2efabcb2dc84e5e001153ed59fad146dad66bbc8e3970b5f0ad2432e","sha256:f6a48425c372a794a31f3e50d152f2ed22d97441fbe1e62bfb8be56c2de86b19"],"state_sha256":"d512ea5c16e164fe49e22ce63ddc0befa32c7f88ad9895fb84d9f6938b003a07"}