{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:53WIKH55HD2VCSA7MU7YF47TPU","short_pith_number":"pith:53WIKH55","canonical_record":{"source":{"id":"2209.15097","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-09-29T21:03:13Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"0faa5fa1e4c4de6a939df399098643849a23ff037bceabf6f7916740e4b2008a","abstract_canon_sha256":"9d66a5b5482999676c43e18a87b82692ca18147f5d7fb3210121a6e3039cba98"},"schema_version":"1.0"},"canonical_sha256":"eeec851fbd38f551481f653f82f3f37d051e50836c7dfe4e315ca55dd52daf05","source":{"kind":"arxiv","id":"2209.15097","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.15097","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2209.15097v2","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.15097","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"53WIKH55HD2V","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"53WIKH55HD2VCSA7","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"53WIKH55","created_at":"2026-07-05T06:14:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:53WIKH55HD2VCSA7MU7YF47TPU","target":"record","payload":{"canonical_record":{"source":{"id":"2209.15097","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-09-29T21:03:13Z","cross_cats_sorted":["cs.LG","math.OC"],"title_canon_sha256":"0faa5fa1e4c4de6a939df399098643849a23ff037bceabf6f7916740e4b2008a","abstract_canon_sha256":"9d66a5b5482999676c43e18a87b82692ca18147f5d7fb3210121a6e3039cba98"},"schema_version":"1.0"},"canonical_sha256":"eeec851fbd38f551481f653f82f3f37d051e50836c7dfe4e315ca55dd52daf05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:14:36.785543Z","signature_b64":"JnRRr6za/MKex2BNK+DqRVBnczsQJtwGF22lb3zR+rh6LfdaD6Nb3yZ9fveEK4DWNFdMBS12jE+vV+K9os7kDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeec851fbd38f551481f653f82f3f37d051e50836c7dfe4e315ca55dd52daf05","last_reissued_at":"2026-07-05T06:14:36.785142Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:14:36.785142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.15097","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9gq0eRBL0IJg4CBv6DfKnDoMLb3D249p1SbLW150mD82kQLXSDF28plBg3KFXiWQq9wHmYnxBL0SVlDoaLC7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:27:32.129756Z"},"content_sha256":"e335985b45fd419f114011e4907d545a711fd43fa463fd038a98ef48a3101ad2","schema_version":"1.0","event_id":"sha256:e335985b45fd419f114011e4907d545a711fd43fa463fd038a98ef48a3101ad2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:53WIKH55HD2VCSA7MU7YF47TPU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Likelihood Adjusted Semidefinite Programs for Clustering Heterogeneous Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Xiaohui Chen, Yubo Zhuang, Yun Yang","submitted_at":"2022-09-29T21:03:13Z","abstract_excerpt":"Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.15097","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.15097/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQxxrfUh/4x3ZX3ueOHpWAQP6omXHJVYfc2/GSvmHoEkUjamF5V5cbX3ISsFTvd1HcCFuIugqODhA5gs399uCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:27:32.130327Z"},"content_sha256":"90d3dcaf742b3d5f54f6a6b5911619a0b3151e061c0f75fca7ce67f096f55ee7","schema_version":"1.0","event_id":"sha256:90d3dcaf742b3d5f54f6a6b5911619a0b3151e061c0f75fca7ce67f096f55ee7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53WIKH55HD2VCSA7MU7YF47TPU/bundle.json","state_url":"https://pith.science/pith/53WIKH55HD2VCSA7MU7YF47TPU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53WIKH55HD2VCSA7MU7YF47TPU/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":"2026-08-04T21:27:32Z","links":{"resolver":"https://pith.science/pith/53WIKH55HD2VCSA7MU7YF47TPU","bundle":"https://pith.science/pith/53WIKH55HD2VCSA7MU7YF47TPU/bundle.json","state":"https://pith.science/pith/53WIKH55HD2VCSA7MU7YF47TPU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53WIKH55HD2VCSA7MU7YF47TPU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:53WIKH55HD2VCSA7MU7YF47TPU","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":"9d66a5b5482999676c43e18a87b82692ca18147f5d7fb3210121a6e3039cba98","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-09-29T21:03:13Z","title_canon_sha256":"0faa5fa1e4c4de6a939df399098643849a23ff037bceabf6f7916740e4b2008a"},"schema_version":"1.0","source":{"id":"2209.15097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.15097","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2209.15097v2","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.15097","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"53WIKH55HD2V","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"53WIKH55HD2VCSA7","created_at":"2026-07-05T06:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"53WIKH55","created_at":"2026-07-05T06:14:36Z"}],"graph_snapshots":[{"event_id":"sha256:90d3dcaf742b3d5f54f6a6b5911619a0b3151e061c0f75fca7ce67f096f55ee7","target":"graph","created_at":"2026-07-05T06:14:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2209.15097/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxi","authors_text":"Xiaohui Chen, Yubo Zhuang, Yun Yang","cross_cats":["cs.LG","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-09-29T21:03:13Z","title":"Likelihood Adjusted Semidefinite Programs for Clustering Heterogeneous Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.15097","kind":"arxiv","version":2},"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:e335985b45fd419f114011e4907d545a711fd43fa463fd038a98ef48a3101ad2","target":"record","created_at":"2026-07-05T06:14:36Z","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":"9d66a5b5482999676c43e18a87b82692ca18147f5d7fb3210121a6e3039cba98","cross_cats_sorted":["cs.LG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-09-29T21:03:13Z","title_canon_sha256":"0faa5fa1e4c4de6a939df399098643849a23ff037bceabf6f7916740e4b2008a"},"schema_version":"1.0","source":{"id":"2209.15097","kind":"arxiv","version":2}},"canonical_sha256":"eeec851fbd38f551481f653f82f3f37d051e50836c7dfe4e315ca55dd52daf05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeec851fbd38f551481f653f82f3f37d051e50836c7dfe4e315ca55dd52daf05","first_computed_at":"2026-07-05T06:14:36.785142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:14:36.785142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JnRRr6za/MKex2BNK+DqRVBnczsQJtwGF22lb3zR+rh6LfdaD6Nb3yZ9fveEK4DWNFdMBS12jE+vV+K9os7kDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:14:36.785543Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.15097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e335985b45fd419f114011e4907d545a711fd43fa463fd038a98ef48a3101ad2","sha256:90d3dcaf742b3d5f54f6a6b5911619a0b3151e061c0f75fca7ce67f096f55ee7"],"state_sha256":"39ac397193775fb644c3036aa1540c81995c7fc779afc9b8a792bfa120c7fb0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ix+PAWAJ3AkBDQK3UftJnMnokYn8teSLBmUk8Sz4ZY24Xh7NGNpCU97kp4ckbLz6F7lkShrT6oj3BXA18ZjpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:27:32.135060Z","bundle_sha256":"aa54b24ff3b949e49892eb02fa6f662142a7fa010233088659648a6b6a11b3c1"}}