{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:P7PN7UYVJ3TF6QYNCHL5NEEO3F","short_pith_number":"pith:P7PN7UYV","canonical_record":{"source":{"id":"1109.3994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-19T10:48:27Z","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"title_canon_sha256":"ee16e683c2553738f274adfb381a2b5f6ce668f9073dc23e803733ecdeeb2348","abstract_canon_sha256":"2ad2d0610b2b808260fc008726d498eb4d85800ad713eedb9394831f0c4d2450"},"schema_version":"1.0"},"canonical_sha256":"7fdedfd3154ee65f430d11d7d6908ed94ec37e1af82b0d6277efd079c5300351","source":{"kind":"arxiv","id":"1109.3994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3994","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3994v1","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3994","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"pith_short_12","alias_value":"P7PN7UYVJ3TF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7PN7UYVJ3TF6QYN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7PN7UYV","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:P7PN7UYVJ3TF6QYNCHL5NEEO3F","target":"record","payload":{"canonical_record":{"source":{"id":"1109.3994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-19T10:48:27Z","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"title_canon_sha256":"ee16e683c2553738f274adfb381a2b5f6ce668f9073dc23e803733ecdeeb2348","abstract_canon_sha256":"2ad2d0610b2b808260fc008726d498eb4d85800ad713eedb9394831f0c4d2450"},"schema_version":"1.0"},"canonical_sha256":"7fdedfd3154ee65f430d11d7d6908ed94ec37e1af82b0d6277efd079c5300351","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.389429Z","signature_b64":"wKk4YoSEVSEDVaSu5b1Z0Uw/y9hxbWwT3G531zSFHJGn5TjWxEfYdev+b4vfbNSJMFSp+JITYqPD5iJ8aaJaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fdedfd3154ee65f430d11d7d6908ed94ec37e1af82b0d6277efd079c5300351","last_reissued_at":"2026-05-18T04:12:45.388858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.388858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.3994","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":"2026-05-18T04:12:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NDRdtwgOVQxoWGhC27GL0vlhuysUzeihcE2KJPRS3MuEPGymOJGnCgp1leETnf6VU028Qaf5v7A0HXRVnKNmAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:36:19.741850Z"},"content_sha256":"8f36a9b7bb4f437493b3868bb4535ca3a05bf3b3efbd383a6f2bbedc4ca3a3b3","schema_version":"1.0","event_id":"sha256:8f36a9b7bb4f437493b3868bb4535ca3a05bf3b3efbd383a6f2bbedc4ca3a3b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:P7PN7UYVJ3TF6QYNCHL5NEEO3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"k-means Approach to the Karhunen-Loeve Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Jacek Tabor, Krzysztof Misztal, Przemyslaw Spurek","submitted_at":"2011-09-19T10:48:27Z","abstract_excerpt":"We present a simultaneous generalization of the well-known Karhunen-Loeve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n=0 we obtain the classical k-means, while for k=1 we obtain PCA algorithm. We show that for some data exploration problems this method gives better result then either of the classical approaches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3994","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":"2026-05-18T04:12:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4WieZeretkgxsQ/teRuD8wfV/CshvY8t10csJYrnM2i7Ujhp2jyJ99p2AyGzDYRVWvUU6veqHlMO24b9n9jBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T14:36:19.742198Z"},"content_sha256":"7186ccbf9f10361ab12231bee20dc50ed1f6b15920e5192a88d1329adaa03b44","schema_version":"1.0","event_id":"sha256:7186ccbf9f10361ab12231bee20dc50ed1f6b15920e5192a88d1329adaa03b44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/bundle.json","state_url":"https://pith.science/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/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":"2026-07-05T14:36:19Z","links":{"resolver":"https://pith.science/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F","bundle":"https://pith.science/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/bundle.json","state":"https://pith.science/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7PN7UYVJ3TF6QYNCHL5NEEO3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:P7PN7UYVJ3TF6QYNCHL5NEEO3F","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":"2ad2d0610b2b808260fc008726d498eb4d85800ad713eedb9394831f0c4d2450","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-19T10:48:27Z","title_canon_sha256":"ee16e683c2553738f274adfb381a2b5f6ce668f9073dc23e803733ecdeeb2348"},"schema_version":"1.0","source":{"id":"1109.3994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.3994","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"arxiv_version","alias_value":"1109.3994v1","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.3994","created_at":"2026-05-18T04:12:45Z"},{"alias_kind":"pith_short_12","alias_value":"P7PN7UYVJ3TF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"P7PN7UYVJ3TF6QYN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"P7PN7UYV","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:7186ccbf9f10361ab12231bee20dc50ed1f6b15920e5192a88d1329adaa03b44","target":"graph","created_at":"2026-05-18T04:12:45Z","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 present a simultaneous generalization of the well-known Karhunen-Loeve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n=0 we obtain the classical k-means, while for k=1 we obtain PCA algorithm. We show that for some data exploration problems this method gives better result then either of the classical approaches.","authors_text":"Jacek Tabor, Krzysztof Misztal, Przemyslaw Spurek","cross_cats":["math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-19T10:48:27Z","title":"k-means Approach to the Karhunen-Loeve Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3994","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":"sha256:8f36a9b7bb4f437493b3868bb4535ca3a05bf3b3efbd383a6f2bbedc4ca3a3b3","target":"record","created_at":"2026-05-18T04:12:45Z","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":"2ad2d0610b2b808260fc008726d498eb4d85800ad713eedb9394831f0c4d2450","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-19T10:48:27Z","title_canon_sha256":"ee16e683c2553738f274adfb381a2b5f6ce668f9073dc23e803733ecdeeb2348"},"schema_version":"1.0","source":{"id":"1109.3994","kind":"arxiv","version":1}},"canonical_sha256":"7fdedfd3154ee65f430d11d7d6908ed94ec37e1af82b0d6277efd079c5300351","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fdedfd3154ee65f430d11d7d6908ed94ec37e1af82b0d6277efd079c5300351","first_computed_at":"2026-05-18T04:12:45.388858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:45.388858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wKk4YoSEVSEDVaSu5b1Z0Uw/y9hxbWwT3G531zSFHJGn5TjWxEfYdev+b4vfbNSJMFSp+JITYqPD5iJ8aaJaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:45.389429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.3994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f36a9b7bb4f437493b3868bb4535ca3a05bf3b3efbd383a6f2bbedc4ca3a3b3","sha256:7186ccbf9f10361ab12231bee20dc50ed1f6b15920e5192a88d1329adaa03b44"],"state_sha256":"73b88bbdd3e63fcc56b1dea110b6858ff6e36de01b09a469bbfe972e06958d8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F85JEF8yPMzaanb+xTVvVOqx33GNnx0FXyeieghoP3YUD07xfiWh+MwioSsZB0jEhBhjfX8KqVvJLsJXd2oUDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T14:36:19.745091Z","bundle_sha256":"f817e8d1d5545cd217bc9c9ca9c49244c667ace39a97caf2522e29e9ac792dce"}}