{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:76UPCU2X3JOAH2S4FUCXZAK2IG","short_pith_number":"pith:76UPCU2X","canonical_record":{"source":{"id":"1905.07389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T17:37:54Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"610b17e8a90788fec716f22a498faa7eebdc06c7648218fd45bc76cd278a8cb9","abstract_canon_sha256":"569bc77d278f64fc6e3c05db181f60ea38d1d22d5dd92042bf243622597c87da"},"schema_version":"1.0"},"canonical_sha256":"ffa8f15357da5c03ea5c2d057c815a4191c06184f3a8d0c2cc846af9a05e701c","source":{"kind":"arxiv","id":"1905.07389","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07389","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07389v1","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07389","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"76UPCU2X3JOA","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"76UPCU2X3JOAH2S4","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"76UPCU2X","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:76UPCU2X3JOAH2S4FUCXZAK2IG","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T17:37:54Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"610b17e8a90788fec716f22a498faa7eebdc06c7648218fd45bc76cd278a8cb9","abstract_canon_sha256":"569bc77d278f64fc6e3c05db181f60ea38d1d22d5dd92042bf243622597c87da"},"schema_version":"1.0"},"canonical_sha256":"ffa8f15357da5c03ea5c2d057c815a4191c06184f3a8d0c2cc846af9a05e701c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:55.741603Z","signature_b64":"zmtQ70AXeMykZHR/+W4Nz3kYIXJonk1Oq/zC5NSKHyTxfnCAOsv9fxUeeYdFLVYOHlca7DOKtqck68Qnl1TtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffa8f15357da5c03ea5c2d057c815a4191c06184f3a8d0c2cc846af9a05e701c","last_reissued_at":"2026-05-17T23:45:55.741162Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:55.741162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07389","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":"2026-05-17T23:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASFP85DIaSRtAo4Uqk5VgT1gO4aSfo4RlosACQAFdPoySgjuWMEujyKj1VNJNSNqXNqI9pOGfXO30Dv2K/4fCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:02:35.711879Z"},"content_sha256":"c1e29e1a7121daa98b59cf69c5fb35a1b61afe1850923f99855d12cb98aef92b","schema_version":"1.0","event_id":"sha256:c1e29e1a7121daa98b59cf69c5fb35a1b61afe1850923f99855d12cb98aef92b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:76UPCU2X3JOAH2S4FUCXZAK2IG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Distributed Estimation of Principal Eigenspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Davoud Ataee Tarzanagh, George Michailidis, Mohamad Kazem Shirani Faradonbeh","submitted_at":"2019-05-17T17:37:54Z","abstract_excerpt":"Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further establish its rate of convergence and show how it relates to the number of nodes employed in the distributed computation, the effective rank of the data matrix under consideration, and the gap in the spectrum of the underlying population covariance matrix. The proposed algorithm is illustrated on low-rank approximation and $\\boldsymbol{k}$-means clustering tasks"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07389","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":"2026-05-17T23:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMIbQOyCVpQBOPfmgMU3gVO71jWdFr5PHY4j/4liTf/biEHswMtv4GILEew4BI3ByJkJ4ytYmpA1bnKCFBcoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:02:35.712229Z"},"content_sha256":"c37ed14260b07bebb1aab816a5c3bdc7bc364c15de25bd305449c3d36973384d","schema_version":"1.0","event_id":"sha256:c37ed14260b07bebb1aab816a5c3bdc7bc364c15de25bd305449c3d36973384d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/bundle.json","state_url":"https://pith.science/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/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":"2026-06-03T19:02:35Z","links":{"resolver":"https://pith.science/pith/76UPCU2X3JOAH2S4FUCXZAK2IG","bundle":"https://pith.science/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/bundle.json","state":"https://pith.science/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76UPCU2X3JOAH2S4FUCXZAK2IG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:76UPCU2X3JOAH2S4FUCXZAK2IG","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":"569bc77d278f64fc6e3c05db181f60ea38d1d22d5dd92042bf243622597c87da","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T17:37:54Z","title_canon_sha256":"610b17e8a90788fec716f22a498faa7eebdc06c7648218fd45bc76cd278a8cb9"},"schema_version":"1.0","source":{"id":"1905.07389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07389","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07389v1","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07389","created_at":"2026-05-17T23:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"76UPCU2X3JOA","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"76UPCU2X3JOAH2S4","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"76UPCU2X","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:c37ed14260b07bebb1aab816a5c3bdc7bc364c15de25bd305449c3d36973384d","target":"graph","created_at":"2026-05-17T23:45:55Z","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 widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further establish its rate of convergence and show how it relates to the number of nodes employed in the distributed computation, the effective rank of the data matrix under consideration, and the gap in the spectrum of the underlying population covariance matrix. The proposed algorithm is illustrated on low-rank approximation and $\\boldsymbol{k}$-means clustering tasks","authors_text":"Davoud Ataee Tarzanagh, George Michailidis, Mohamad Kazem Shirani Faradonbeh","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T17:37:54Z","title":"Online Distributed Estimation of Principal Eigenspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07389","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:c1e29e1a7121daa98b59cf69c5fb35a1b61afe1850923f99855d12cb98aef92b","target":"record","created_at":"2026-05-17T23:45:55Z","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":"569bc77d278f64fc6e3c05db181f60ea38d1d22d5dd92042bf243622597c87da","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2019-05-17T17:37:54Z","title_canon_sha256":"610b17e8a90788fec716f22a498faa7eebdc06c7648218fd45bc76cd278a8cb9"},"schema_version":"1.0","source":{"id":"1905.07389","kind":"arxiv","version":1}},"canonical_sha256":"ffa8f15357da5c03ea5c2d057c815a4191c06184f3a8d0c2cc846af9a05e701c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffa8f15357da5c03ea5c2d057c815a4191c06184f3a8d0c2cc846af9a05e701c","first_computed_at":"2026-05-17T23:45:55.741162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:55.741162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zmtQ70AXeMykZHR/+W4Nz3kYIXJonk1Oq/zC5NSKHyTxfnCAOsv9fxUeeYdFLVYOHlca7DOKtqck68Qnl1TtDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:55.741603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e29e1a7121daa98b59cf69c5fb35a1b61afe1850923f99855d12cb98aef92b","sha256:c37ed14260b07bebb1aab816a5c3bdc7bc364c15de25bd305449c3d36973384d"],"state_sha256":"3b99459765f8ffa0de5de24e245dd3095823a45a8bc1d5be587ed7b567245292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ckb4B0cpA3GSCMpGP/dpnahHM832HBmxqM1b9KZEyaNX3NZhcB+meD+ZyVhf9niIp0Wn2u0yMlLnr6cfFL9PAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:02:35.714193Z","bundle_sha256":"398c17c68c82606a5bd5c8c3a7c1c78d7fe59db51219f6d1823878bb412b95e4"}}