{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KH26G4WYD5RMT2N27MMFFS46TJ","short_pith_number":"pith:KH26G4WY","canonical_record":{"source":{"id":"1412.4044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-12T16:32:48Z","cross_cats_sorted":["cs.CV","cs.NA","math.OC"],"title_canon_sha256":"23d8459c8d74dd38a56e5386b9daba9b50a51128fbb8f26de8096046e3de6d88","abstract_canon_sha256":"afb8d8a720288de733aac59151d51456dadbb9af9dda778d7f97ca68a41e1efa"},"schema_version":"1.0"},"canonical_sha256":"51f5e372d81f62c9e9bafb1852cb9e9a7ef1e896ac0bcb43f8f893183b57f927","source":{"kind":"arxiv","id":"1412.4044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4044","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4044v2","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4044","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"KH26G4WYD5RM","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KH26G4WYD5RMT2N2","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KH26G4WY","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KH26G4WYD5RMT2N27MMFFS46TJ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-12T16:32:48Z","cross_cats_sorted":["cs.CV","cs.NA","math.OC"],"title_canon_sha256":"23d8459c8d74dd38a56e5386b9daba9b50a51128fbb8f26de8096046e3de6d88","abstract_canon_sha256":"afb8d8a720288de733aac59151d51456dadbb9af9dda778d7f97ca68a41e1efa"},"schema_version":"1.0"},"canonical_sha256":"51f5e372d81f62c9e9bafb1852cb9e9a7ef1e896ac0bcb43f8f893183b57f927","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:31.289684Z","signature_b64":"Yrrembu324TxiPhOr6neaDUx0pilKtEl5i6TLPachKKi7RRbFSzSiQh6Yn+gZl4JkN0Gcj9hMkK9eSE/lki7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f5e372d81f62c9e9bafb1852cb9e9a7ef1e896ac0bcb43f8f893183b57f927","last_reissued_at":"2026-05-18T02:18:31.289252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:31.289252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4044","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":"2026-05-18T02:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xja1Kcl7/9yj4QZlvCMYp25XzkDltK8hBpCKtZ19B6aFHDHF3eu5zwdJIsCccPBM3FfSY4+JWfj2teHpe0K9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:22:11.136937Z"},"content_sha256":"50911dd1016cac2f94e090f153489851be2d0fce5cf82618b7df3e058b421a33","schema_version":"1.0","event_id":"sha256:50911dd1016cac2f94e090f153489851be2d0fce5cf82618b7df3e058b421a33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KH26G4WYD5RMT2N27MMFFS46TJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Stochastic Gradient Descent on the Grassmannian for Robust Low-Rank Subspace Recovery and Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.OC"],"primary_cat":"stat.ML","authors_text":"Jun He, Yue Zhang","submitted_at":"2014-12-12T16:32:48Z","abstract_excerpt":"In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix $L_{2,1}$ norm minimization with rank constraint problem as a stochastic optimization approach constrained on Grassmann manifold. For each observed data vector, the low-rank subspace $\\mathcal{S}$ is updated by taking a gradient step along the geodesic of Grassmannian. In order to accelerate the convergence rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4044","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":"2026-05-18T02:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7/n/wJpMpfE4ePL8HVUl3xfmBymS9oCRxxuPVTVNcV3MaRlrxbFlqP2PKvm2SO2i9phz55LF7lYe80I7legDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:22:11.137536Z"},"content_sha256":"a6ebe715b6f49867df585e2272ce142c0104c01753d5a3bf743ad2b1832675e5","schema_version":"1.0","event_id":"sha256:a6ebe715b6f49867df585e2272ce142c0104c01753d5a3bf743ad2b1832675e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KH26G4WYD5RMT2N27MMFFS46TJ/bundle.json","state_url":"https://pith.science/pith/KH26G4WYD5RMT2N27MMFFS46TJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KH26G4WYD5RMT2N27MMFFS46TJ/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":"2026-05-25T21:22:11Z","links":{"resolver":"https://pith.science/pith/KH26G4WYD5RMT2N27MMFFS46TJ","bundle":"https://pith.science/pith/KH26G4WYD5RMT2N27MMFFS46TJ/bundle.json","state":"https://pith.science/pith/KH26G4WYD5RMT2N27MMFFS46TJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KH26G4WYD5RMT2N27MMFFS46TJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KH26G4WYD5RMT2N27MMFFS46TJ","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":"afb8d8a720288de733aac59151d51456dadbb9af9dda778d7f97ca68a41e1efa","cross_cats_sorted":["cs.CV","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-12T16:32:48Z","title_canon_sha256":"23d8459c8d74dd38a56e5386b9daba9b50a51128fbb8f26de8096046e3de6d88"},"schema_version":"1.0","source":{"id":"1412.4044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4044","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4044v2","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4044","created_at":"2026-05-18T02:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"KH26G4WYD5RM","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KH26G4WYD5RMT2N2","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KH26G4WY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:a6ebe715b6f49867df585e2272ce142c0104c01753d5a3bf743ad2b1832675e5","target":"graph","created_at":"2026-05-18T02:18:31Z","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":"In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix $L_{2,1}$ norm minimization with rank constraint problem as a stochastic optimization approach constrained on Grassmann manifold. For each observed data vector, the low-rank subspace $\\mathcal{S}$ is updated by taking a gradient step along the geodesic of Grassmannian. In order to accelerate the convergence rat","authors_text":"Jun He, Yue Zhang","cross_cats":["cs.CV","cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-12T16:32:48Z","title":"Adaptive Stochastic Gradient Descent on the Grassmannian for Robust Low-Rank Subspace Recovery and Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4044","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":"sha256:50911dd1016cac2f94e090f153489851be2d0fce5cf82618b7df3e058b421a33","target":"record","created_at":"2026-05-18T02:18:31Z","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":"afb8d8a720288de733aac59151d51456dadbb9af9dda778d7f97ca68a41e1efa","cross_cats_sorted":["cs.CV","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-12T16:32:48Z","title_canon_sha256":"23d8459c8d74dd38a56e5386b9daba9b50a51128fbb8f26de8096046e3de6d88"},"schema_version":"1.0","source":{"id":"1412.4044","kind":"arxiv","version":2}},"canonical_sha256":"51f5e372d81f62c9e9bafb1852cb9e9a7ef1e896ac0bcb43f8f893183b57f927","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f5e372d81f62c9e9bafb1852cb9e9a7ef1e896ac0bcb43f8f893183b57f927","first_computed_at":"2026-05-18T02:18:31.289252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:31.289252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yrrembu324TxiPhOr6neaDUx0pilKtEl5i6TLPachKKi7RRbFSzSiQh6Yn+gZl4JkN0Gcj9hMkK9eSE/lki7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:31.289684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50911dd1016cac2f94e090f153489851be2d0fce5cf82618b7df3e058b421a33","sha256:a6ebe715b6f49867df585e2272ce142c0104c01753d5a3bf743ad2b1832675e5"],"state_sha256":"c638b0c1e8e87a01f6348409f3038b39505813710c6287b9d7ff1f34a3fcc522"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WwP7x1TX10qH4S7qm5Hrs4ojYksAx5XCRwcOYjci+ZnHEdyQY6cdLYYf0CfJt3DHhajeTW5WeVo1ziICq5NfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:22:11.140736Z","bundle_sha256":"6088a326afbf34c1e096ec945c4164272b8ff6c21bbd8dc529b54ad9f70de546"}}