{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WBDH255HKE5ILLTQXFJM7AVOFP","short_pith_number":"pith:WBDH255H","canonical_record":{"source":{"id":"1506.01490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-04T07:36:57Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"20a95faca3fe7b2ad2f3584bff1b01aa48bd79eee4320e559be9076f443825d3","abstract_canon_sha256":"5233e16af76b1b45b123bc68ff3508f18aad3ba6553593e5f3d3795b3f50e50f"},"schema_version":"1.0"},"canonical_sha256":"b0467d77a7513a85ae70b952cf82ae2bc8eccb248ddfd4d5f8459f3fdb61a509","source":{"kind":"arxiv","id":"1506.01490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01490","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01490v2","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01490","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"WBDH255HKE5I","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WBDH255HKE5ILLTQ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WBDH255H","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WBDH255HKE5ILLTQXFJM7AVOFP","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-04T07:36:57Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"20a95faca3fe7b2ad2f3584bff1b01aa48bd79eee4320e559be9076f443825d3","abstract_canon_sha256":"5233e16af76b1b45b123bc68ff3508f18aad3ba6553593e5f3d3795b3f50e50f"},"schema_version":"1.0"},"canonical_sha256":"b0467d77a7513a85ae70b952cf82ae2bc8eccb248ddfd4d5f8459f3fdb61a509","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:34.492119Z","signature_b64":"vvn3lbYut2KVIM4QdzblMlezz4vjOSvwLy/B/KZIXrnyd/1JdxftoxyNwWZwe+aah/o1QkAP9qaYFg6jT6GoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0467d77a7513a85ae70b952cf82ae2bc8eccb248ddfd4d5f8459f3fdb61a509","last_reissued_at":"2026-05-18T01:30:34.491420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:34.491420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01490","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":"2026-05-18T01:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EIeCtQDhk9l8yTIy5EewRYfigdXoWi+OHEFoI6HHdHwOeEbFl2bTE1JsCAqEC9ULmEyC/itAMGCKBF2xG2kSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:02:38.258112Z"},"content_sha256":"d2a8e7aaace6de7f64139d128bd4b0c2a207c39ef02217edf79b63b78edaee39","schema_version":"1.0","event_id":"sha256:d2a8e7aaace6de7f64139d128bd4b0c2a207c39ef02217edf79b63b78edaee39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WBDH255HKE5ILLTQXFJM7AVOFP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rivalry of Two Families of Algorithms for Memory-Restricted Streaming PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Chi-Jen Lu, Chun-Liang Li, Hsuan-Tien Lin","submitted_at":"2015-06-04T07:36:57Z","abstract_excerpt":"We study the problem of recovering the subspace spanned by the first $k$ principal components of $d$-dimensional data under the streaming setting, with a memory bound of $O(kd)$. Two families of algorithms are known for this problem. The first family is based on the framework of stochastic gradient descent. Nevertheless, the convergence rate of the family can be seriously affected by the learning rate of the descent steps and deserves more serious study. The second family is based on the power method over blocks of data, but setting the block size for its existing algorithms is not an easy tas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01490","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":""},"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":"2026-05-18T01:30:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbkqFvTkNc4At0xDSAeMbHhF6CnIRuJZeetbz6DOYnazYAQGhehyTC6LMlQzba3HhByZfucDrNIJLecaow46Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:02:38.258816Z"},"content_sha256":"d73000a35b44305ced8b034556092ef4cebbb39c04fb6278f5f9bb581d12b748","schema_version":"1.0","event_id":"sha256:d73000a35b44305ced8b034556092ef4cebbb39c04fb6278f5f9bb581d12b748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WBDH255HKE5ILLTQXFJM7AVOFP/bundle.json","state_url":"https://pith.science/pith/WBDH255HKE5ILLTQXFJM7AVOFP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WBDH255HKE5ILLTQXFJM7AVOFP/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":"2026-05-25T15:02:38Z","links":{"resolver":"https://pith.science/pith/WBDH255HKE5ILLTQXFJM7AVOFP","bundle":"https://pith.science/pith/WBDH255HKE5ILLTQXFJM7AVOFP/bundle.json","state":"https://pith.science/pith/WBDH255HKE5ILLTQXFJM7AVOFP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WBDH255HKE5ILLTQXFJM7AVOFP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WBDH255HKE5ILLTQXFJM7AVOFP","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":"5233e16af76b1b45b123bc68ff3508f18aad3ba6553593e5f3d3795b3f50e50f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-04T07:36:57Z","title_canon_sha256":"20a95faca3fe7b2ad2f3584bff1b01aa48bd79eee4320e559be9076f443825d3"},"schema_version":"1.0","source":{"id":"1506.01490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01490","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01490v2","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01490","created_at":"2026-05-18T01:30:34Z"},{"alias_kind":"pith_short_12","alias_value":"WBDH255HKE5I","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WBDH255HKE5ILLTQ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WBDH255H","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:d73000a35b44305ced8b034556092ef4cebbb39c04fb6278f5f9bb581d12b748","target":"graph","created_at":"2026-05-18T01:30:34Z","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 study the problem of recovering the subspace spanned by the first $k$ principal components of $d$-dimensional data under the streaming setting, with a memory bound of $O(kd)$. Two families of algorithms are known for this problem. The first family is based on the framework of stochastic gradient descent. Nevertheless, the convergence rate of the family can be seriously affected by the learning rate of the descent steps and deserves more serious study. The second family is based on the power method over blocks of data, but setting the block size for its existing algorithms is not an easy tas","authors_text":"Chi-Jen Lu, Chun-Liang Li, Hsuan-Tien Lin","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-04T07:36:57Z","title":"Rivalry of Two Families of Algorithms for Memory-Restricted Streaming PCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01490","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:d2a8e7aaace6de7f64139d128bd4b0c2a207c39ef02217edf79b63b78edaee39","target":"record","created_at":"2026-05-18T01:30:34Z","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":"5233e16af76b1b45b123bc68ff3508f18aad3ba6553593e5f3d3795b3f50e50f","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-04T07:36:57Z","title_canon_sha256":"20a95faca3fe7b2ad2f3584bff1b01aa48bd79eee4320e559be9076f443825d3"},"schema_version":"1.0","source":{"id":"1506.01490","kind":"arxiv","version":2}},"canonical_sha256":"b0467d77a7513a85ae70b952cf82ae2bc8eccb248ddfd4d5f8459f3fdb61a509","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0467d77a7513a85ae70b952cf82ae2bc8eccb248ddfd4d5f8459f3fdb61a509","first_computed_at":"2026-05-18T01:30:34.491420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:34.491420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vvn3lbYut2KVIM4QdzblMlezz4vjOSvwLy/B/KZIXrnyd/1JdxftoxyNwWZwe+aah/o1QkAP9qaYFg6jT6GoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:34.492119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2a8e7aaace6de7f64139d128bd4b0c2a207c39ef02217edf79b63b78edaee39","sha256:d73000a35b44305ced8b034556092ef4cebbb39c04fb6278f5f9bb581d12b748"],"state_sha256":"e6a524218b410e69bc194a8998cbe1923dfbe538a352f7dd8a171d0b083f8536"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMxLuQ20u0wiiStbh3ULL2d63IPZxgJvb0Dy5Yt5+GhB90C6mndfwkEYOJ69dHzw2xlaa1kcYOJNvys7B1QKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:02:38.262840Z","bundle_sha256":"39de0c68d224ca3d3a0b8edc4b8315a8b54ff38e10c55279a19d16978e22be7f"}}