{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WB2SBO2PDXOPYFEJTHGFZYJZGV","short_pith_number":"pith:WB2SBO2P","canonical_record":{"source":{"id":"1410.0342","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-01T19:31:40Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"2834a175ad0c8b8da574f7e3a9bbcbcd027f7faf960dfd275e5fe4af3ba6b7e1","abstract_canon_sha256":"2342151be7e51ddd15bd1b20fbf0b8ab8b3efb6d72f73580b011adea2dcca456"},"schema_version":"1.0"},"canonical_sha256":"b07520bb4f1ddcfc148999cc5ce139356fda25c081fd3a5f9aad8615ed1a3e91","source":{"kind":"arxiv","id":"1410.0342","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0342","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0342v4","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0342","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"WB2SBO2PDXOP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WB2SBO2PDXOPYFEJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WB2SBO2P","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WB2SBO2PDXOPYFEJTHGFZYJZGV","target":"record","payload":{"canonical_record":{"source":{"id":"1410.0342","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-01T19:31:40Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"2834a175ad0c8b8da574f7e3a9bbcbcd027f7faf960dfd275e5fe4af3ba6b7e1","abstract_canon_sha256":"2342151be7e51ddd15bd1b20fbf0b8ab8b3efb6d72f73580b011adea2dcca456"},"schema_version":"1.0"},"canonical_sha256":"b07520bb4f1ddcfc148999cc5ce139356fda25c081fd3a5f9aad8615ed1a3e91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:01.126058Z","signature_b64":"bLVNga8YJbe7qKVXGYnoQxSTEnvNfR5f4bwyxUIGfA64nPzVgG047NOT4M7CtB4Qd6LAobhAacX9S4evDWbWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b07520bb4f1ddcfc148999cc5ce139356fda25c081fd3a5f9aad8615ed1a3e91","last_reissued_at":"2026-05-18T02:17:01.125337Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:01.125337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.0342","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ethw5dngoBAXFrOdXZNX49/hbNN0JGtYjjFVUvbPT82IGtxB89eOeTttkdcxxLpgGuFMYQkOUpL9/S/cCldoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:23.599159Z"},"content_sha256":"f991ccfb068b26f11749b3c5d423657f0000a95e212c8d176d0e65bcfe645ccf","schema_version":"1.0","event_id":"sha256:f991ccfb068b26f11749b3c5d423657f0000a95e212c8d176d0e65bcfe645ccf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WB2SBO2PDXOPYFEJTHGFZYJZGV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Low Rank Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Corinne Horn, Madeleine Udell, Reza Zadeh, Stephen Boyd","submitted_at":"2014-10-01T19:31:40Z","abstract_excerpt":"Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0342","kind":"arxiv","version":4},"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":"2026-05-18T02:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R7Ef3aaww7HUVPnfZidMeUYOk2UHEPj58XwjW8PrjNIqzGwencyCqpbNueUaDWT+LGmDAYbNmxiEVazGb6ylDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:23.599804Z"},"content_sha256":"8a51cb0568708a0578f0ca24e74b9b7e1c036b09106405305bd508f202a85a0b","schema_version":"1.0","event_id":"sha256:8a51cb0568708a0578f0ca24e74b9b7e1c036b09106405305bd508f202a85a0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/bundle.json","state_url":"https://pith.science/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/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":"2026-05-30T02:37:23Z","links":{"resolver":"https://pith.science/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV","bundle":"https://pith.science/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/bundle.json","state":"https://pith.science/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WB2SBO2PDXOPYFEJTHGFZYJZGV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WB2SBO2PDXOPYFEJTHGFZYJZGV","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":"2342151be7e51ddd15bd1b20fbf0b8ab8b3efb6d72f73580b011adea2dcca456","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-01T19:31:40Z","title_canon_sha256":"2834a175ad0c8b8da574f7e3a9bbcbcd027f7faf960dfd275e5fe4af3ba6b7e1"},"schema_version":"1.0","source":{"id":"1410.0342","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0342","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0342v4","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0342","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"WB2SBO2PDXOP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WB2SBO2PDXOPYFEJ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WB2SBO2P","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:8a51cb0568708a0578f0ca24e74b9b7e1c036b09106405305bd508f202a85a0b","target":"graph","created_at":"2026-05-18T02:17:01Z","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":"Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, $k$-means, $k$-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing","authors_text":"Corinne Horn, Madeleine Udell, Reza Zadeh, Stephen Boyd","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-01T19:31:40Z","title":"Generalized Low Rank Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0342","kind":"arxiv","version":4},"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:f991ccfb068b26f11749b3c5d423657f0000a95e212c8d176d0e65bcfe645ccf","target":"record","created_at":"2026-05-18T02:17:01Z","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":"2342151be7e51ddd15bd1b20fbf0b8ab8b3efb6d72f73580b011adea2dcca456","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-10-01T19:31:40Z","title_canon_sha256":"2834a175ad0c8b8da574f7e3a9bbcbcd027f7faf960dfd275e5fe4af3ba6b7e1"},"schema_version":"1.0","source":{"id":"1410.0342","kind":"arxiv","version":4}},"canonical_sha256":"b07520bb4f1ddcfc148999cc5ce139356fda25c081fd3a5f9aad8615ed1a3e91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b07520bb4f1ddcfc148999cc5ce139356fda25c081fd3a5f9aad8615ed1a3e91","first_computed_at":"2026-05-18T02:17:01.125337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:01.125337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLVNga8YJbe7qKVXGYnoQxSTEnvNfR5f4bwyxUIGfA64nPzVgG047NOT4M7CtB4Qd6LAobhAacX9S4evDWbWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:01.126058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0342","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f991ccfb068b26f11749b3c5d423657f0000a95e212c8d176d0e65bcfe645ccf","sha256:8a51cb0568708a0578f0ca24e74b9b7e1c036b09106405305bd508f202a85a0b"],"state_sha256":"6148dd96f95d62da539cf877e724d57b0005beb104244534d83ce34076e77bc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MW3MJh4wAhgU60ViUums/qphiGa/FLg1R6zbF8OwrOJSXLUrjTG9J9Z1+4GeNqBUN2cy0AEIkRpObluUj2bAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:37:23.602933Z","bundle_sha256":"90a0b1eb64084db97907098cf75b5931e09b9290c0d0d252620994c431ba8d9d"}}