{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:KNVORKTFBMOBB5QTMPQGX6WXFO","short_pith_number":"pith:KNVORKTF","canonical_record":{"source":{"id":"2103.13523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-24T23:11:32Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"5d1fab785c0a4c03cb5781cffc417c214e47bd8ef712913294799e4c3ca4e504","abstract_canon_sha256":"638e25ff52bc68a6fa0fda97904bd0d524e6c8f8c64230eadaf95b8cf79027b9"},"schema_version":"1.0"},"canonical_sha256":"536ae8aa650b1c10f61363e06bfad72bbb19770fcabea98bb96c1defe16819b4","source":{"kind":"arxiv","id":"2103.13523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.13523","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"2103.13523v1","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.13523","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"KNVORKTFBMOB","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_16","alias_value":"KNVORKTFBMOBB5QT","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_8","alias_value":"KNVORKTF","created_at":"2026-07-05T02:26:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:KNVORKTFBMOBB5QTMPQGX6WXFO","target":"record","payload":{"canonical_record":{"source":{"id":"2103.13523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-24T23:11:32Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"5d1fab785c0a4c03cb5781cffc417c214e47bd8ef712913294799e4c3ca4e504","abstract_canon_sha256":"638e25ff52bc68a6fa0fda97904bd0d524e6c8f8c64230eadaf95b8cf79027b9"},"schema_version":"1.0"},"canonical_sha256":"536ae8aa650b1c10f61363e06bfad72bbb19770fcabea98bb96c1defe16819b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:26:19.899288Z","signature_b64":"5M48hIPwx7BVrltGoG0hwdwkty3pkzf07NibaTZg+MxbWdlJ6jIznpe9ZT+DuAIi735/HsCQqk+UvFo7pNDTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"536ae8aa650b1c10f61363e06bfad72bbb19770fcabea98bb96c1defe16819b4","last_reissued_at":"2026-07-05T02:26:19.898893Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:26:19.898893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.13523","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":"2026-07-05T02:26:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dvoAIZzvX2PdxB/yTRod2wyHy2dKKfkkUUJaBmaiwqLkKiryagoqTJPXnYBRmhb5bKEL2Xj3oQ1nuTh9st1iBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:01:25.346807Z"},"content_sha256":"59f05bc31f482e705cb8d19e8aaa8c31493fb3d8ea76a0d55a58175c9c3738eb","schema_version":"1.0","event_id":"sha256:59f05bc31f482e705cb8d19e8aaa8c31493fb3d8ea76a0d55a58175c9c3738eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:KNVORKTFBMOBB5QTMPQGX6WXFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Aleksandr Aravkin, Hexuan Liu","submitted_at":"2021-03-24T23:11:32Z","abstract_excerpt":"A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading eigenvectors with sparsity constraints simultaneously. We establish numerical convergence results for the proposed algorithms using a perturbation framework, and extend our analysis to other existing alternatives for sparse eigenvector estimation. We then apply our algorithms to solve the sparse principle component analysis problem for a wide range of test dataset"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.13523","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.13523/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":"2026-07-05T02:26:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qSsr0ZTHilUAJQoSpqAeHNPEV5ye24BidaniDYVGqSU07kNJMebKT17NGSsWNtPHt3ZO1Ar7vsduLTqF1AtVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:01:25.347399Z"},"content_sha256":"38c09f8ea629ba7249e5ef7d42c3f8d574fee569d3f3b0cdfb13fa548d158a2a","schema_version":"1.0","event_id":"sha256:38c09f8ea629ba7249e5ef7d42c3f8d574fee569d3f3b0cdfb13fa548d158a2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/bundle.json","state_url":"https://pith.science/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/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":"2026-08-15T07:01:25Z","links":{"resolver":"https://pith.science/pith/KNVORKTFBMOBB5QTMPQGX6WXFO","bundle":"https://pith.science/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/bundle.json","state":"https://pith.science/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNVORKTFBMOBB5QTMPQGX6WXFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:KNVORKTFBMOBB5QTMPQGX6WXFO","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":"638e25ff52bc68a6fa0fda97904bd0d524e6c8f8c64230eadaf95b8cf79027b9","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-24T23:11:32Z","title_canon_sha256":"5d1fab785c0a4c03cb5781cffc417c214e47bd8ef712913294799e4c3ca4e504"},"schema_version":"1.0","source":{"id":"2103.13523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.13523","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"arxiv_version","alias_value":"2103.13523v1","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.13523","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_12","alias_value":"KNVORKTFBMOB","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_16","alias_value":"KNVORKTFBMOBB5QT","created_at":"2026-07-05T02:26:19Z"},{"alias_kind":"pith_short_8","alias_value":"KNVORKTF","created_at":"2026-07-05T02:26:19Z"}],"graph_snapshots":[{"event_id":"sha256:38c09f8ea629ba7249e5ef7d42c3f8d574fee569d3f3b0cdfb13fa548d158a2a","target":"graph","created_at":"2026-07-05T02:26:19Z","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/2103.13523/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading eigenvectors with sparsity constraints simultaneously. We establish numerical convergence results for the proposed algorithms using a perturbation framework, and extend our analysis to other existing alternatives for sparse eigenvector estimation. We then apply our algorithms to solve the sparse principle component analysis problem for a wide range of test dataset","authors_text":"Aleksandr Aravkin, Hexuan Liu","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-24T23:11:32Z","title":"Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.13523","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":"sha256:59f05bc31f482e705cb8d19e8aaa8c31493fb3d8ea76a0d55a58175c9c3738eb","target":"record","created_at":"2026-07-05T02:26:19Z","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":"638e25ff52bc68a6fa0fda97904bd0d524e6c8f8c64230eadaf95b8cf79027b9","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-03-24T23:11:32Z","title_canon_sha256":"5d1fab785c0a4c03cb5781cffc417c214e47bd8ef712913294799e4c3ca4e504"},"schema_version":"1.0","source":{"id":"2103.13523","kind":"arxiv","version":1}},"canonical_sha256":"536ae8aa650b1c10f61363e06bfad72bbb19770fcabea98bb96c1defe16819b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"536ae8aa650b1c10f61363e06bfad72bbb19770fcabea98bb96c1defe16819b4","first_computed_at":"2026-07-05T02:26:19.898893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:26:19.898893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5M48hIPwx7BVrltGoG0hwdwkty3pkzf07NibaTZg+MxbWdlJ6jIznpe9ZT+DuAIi735/HsCQqk+UvFo7pNDTDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:26:19.899288Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.13523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59f05bc31f482e705cb8d19e8aaa8c31493fb3d8ea76a0d55a58175c9c3738eb","sha256:38c09f8ea629ba7249e5ef7d42c3f8d574fee569d3f3b0cdfb13fa548d158a2a"],"state_sha256":"01f8f113a991df017ed557438ee31e52ed6adc380143936d252efbe0d3b9fa4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lEf7Pqu5srXlcqoK+D5nyu9pXw9WiSMqVvLtazApm7cOhd9pRSmrMCfs6vZV2kNCq37pLsjCimZOllStTU7yBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T07:01:25.352835Z","bundle_sha256":"d918a8916f970e5cf7a8666b682e87639da95b7621606635f7445f9a601c64dd"}}