{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GZMKCQJRWMVPYL4SJCS6ANABC5","short_pith_number":"pith:GZMKCQJR","canonical_record":{"source":{"id":"1712.07242","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-19T22:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"0bc21311780f75876641e4bf72a2809b67ce6295cd6bacad7e88eea6ab4d9c79","abstract_canon_sha256":"c3fa85aad4bf7af61184994c925d3f77e8207ef4c495187779539ee919ee231e"},"schema_version":"1.0"},"canonical_sha256":"3658a14131b32afc2f9248a5e034011755e4f61a0a0882dd6ee8c59ac8748978","source":{"kind":"arxiv","id":"1712.07242","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07242","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07242v3","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07242","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"GZMKCQJRWMVP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZMKCQJRWMVPYL4S","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZMKCQJR","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GZMKCQJRWMVPYL4SJCS6ANABC5","target":"record","payload":{"canonical_record":{"source":{"id":"1712.07242","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-19T22:23:53Z","cross_cats_sorted":[],"title_canon_sha256":"0bc21311780f75876641e4bf72a2809b67ce6295cd6bacad7e88eea6ab4d9c79","abstract_canon_sha256":"c3fa85aad4bf7af61184994c925d3f77e8207ef4c495187779539ee919ee231e"},"schema_version":"1.0"},"canonical_sha256":"3658a14131b32afc2f9248a5e034011755e4f61a0a0882dd6ee8c59ac8748978","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:10.459297Z","signature_b64":"capgLTwVec/e16V1GweFXwf/bqAtA/JCuHISlVXMIciEc/PM4LOxL95YUZ44tSBTO2q/Emr0RYBfyX/wiqIyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3658a14131b32afc2f9248a5e034011755e4f61a0a0882dd6ee8c59ac8748978","last_reissued_at":"2026-05-18T00:22:10.458776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:10.458776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.07242","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvGG8TDSxNKaqIKOVsiJcZSXiELk8DVGt7BLS2ZDqfNWdvFviUIM7sc3wTysegDX8NL5QSuypGkkffXW/zSCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:03:19.561293Z"},"content_sha256":"f4f2fc256e07e52e785f1033cf8c0f397631d1624d9df0a2f41f9ff828adaa94","schema_version":"1.0","event_id":"sha256:f4f2fc256e07e52e785f1033cf8c0f397631d1624d9df0a2f41f9ff828adaa94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GZMKCQJRWMVPYL4SJCS6ANABC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Time Clustering for High Dimensional Mixtures of Gaussian Clouds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Dan Kushnir, Iraj Saniee, Shirin Jalali","submitted_at":"2017-12-19T22:23:53Z","abstract_excerpt":"Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused primarily on improving separation bounds and their generalization to arbitrary classes of mixture models, less emphasis has been paid to practical computational efficiency of the proposed solutions. In this paper, we propose a novel and highly efficient clustering algorithm for $n$ points drawn from a mixture of two arbitrary Gaussian distributions in $\\mathbb{R}^p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07242","kind":"arxiv","version":3},"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":"2026-05-18T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gnuBz9Nj5aMZwXFGpHoTeDqdrmU4ITZKgd9iwcODUvGqbldAg0+/+4ncf/vEzKFZcnPqf3xEXyUmLyUa//QAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T21:03:19.561684Z"},"content_sha256":"42bc11943dcf5416dab417ec76330ca3a354c1e3bb6ea9c9debf2c4a4ab9515c","schema_version":"1.0","event_id":"sha256:42bc11943dcf5416dab417ec76330ca3a354c1e3bb6ea9c9debf2c4a4ab9515c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/bundle.json","state_url":"https://pith.science/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/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":"2026-06-09T21:03:19Z","links":{"resolver":"https://pith.science/pith/GZMKCQJRWMVPYL4SJCS6ANABC5","bundle":"https://pith.science/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/bundle.json","state":"https://pith.science/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZMKCQJRWMVPYL4SJCS6ANABC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GZMKCQJRWMVPYL4SJCS6ANABC5","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":"c3fa85aad4bf7af61184994c925d3f77e8207ef4c495187779539ee919ee231e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-19T22:23:53Z","title_canon_sha256":"0bc21311780f75876641e4bf72a2809b67ce6295cd6bacad7e88eea6ab4d9c79"},"schema_version":"1.0","source":{"id":"1712.07242","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.07242","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1712.07242v3","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.07242","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"GZMKCQJRWMVP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZMKCQJRWMVPYL4S","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZMKCQJR","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:42bc11943dcf5416dab417ec76330ca3a354c1e3bb6ea9c9debf2c4a4ab9515c","target":"graph","created_at":"2026-05-18T00:22:10Z","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":"Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused primarily on improving separation bounds and their generalization to arbitrary classes of mixture models, less emphasis has been paid to practical computational efficiency of the proposed solutions. In this paper, we propose a novel and highly efficient clustering algorithm for $n$ points drawn from a mixture of two arbitrary Gaussian distributions in $\\mathbb{R}^p","authors_text":"Dan Kushnir, Iraj Saniee, Shirin Jalali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-19T22:23:53Z","title":"Linear Time Clustering for High Dimensional Mixtures of Gaussian Clouds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07242","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:f4f2fc256e07e52e785f1033cf8c0f397631d1624d9df0a2f41f9ff828adaa94","target":"record","created_at":"2026-05-18T00:22:10Z","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":"c3fa85aad4bf7af61184994c925d3f77e8207ef4c495187779539ee919ee231e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-19T22:23:53Z","title_canon_sha256":"0bc21311780f75876641e4bf72a2809b67ce6295cd6bacad7e88eea6ab4d9c79"},"schema_version":"1.0","source":{"id":"1712.07242","kind":"arxiv","version":3}},"canonical_sha256":"3658a14131b32afc2f9248a5e034011755e4f61a0a0882dd6ee8c59ac8748978","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3658a14131b32afc2f9248a5e034011755e4f61a0a0882dd6ee8c59ac8748978","first_computed_at":"2026-05-18T00:22:10.458776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:10.458776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"capgLTwVec/e16V1GweFXwf/bqAtA/JCuHISlVXMIciEc/PM4LOxL95YUZ44tSBTO2q/Emr0RYBfyX/wiqIyBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:10.459297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.07242","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f2fc256e07e52e785f1033cf8c0f397631d1624d9df0a2f41f9ff828adaa94","sha256:42bc11943dcf5416dab417ec76330ca3a354c1e3bb6ea9c9debf2c4a4ab9515c"],"state_sha256":"e124d04e0e35c7f621b46531ed8646d2b8f9ffab3c25e7e85864d9596f542cac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qY9dViBMf11MJAO923354LyVIzv9VMMtpNsDEE5VhsvpW78/2UPsbTPnqIR+n9Y1irCjlsOA8RWtVRiV9IjEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T21:03:19.564578Z","bundle_sha256":"6d0883e5c0e472d3457e9a3e4972a3da97b89054dd623c80a24277c0e90b1156"}}