{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HDHSOC565CXSJGAUQJS53CSTKD","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":"822030c844e395a62201eab8435d49829d0a805e75f272d02ba3da1fffc90289","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-23T06:10:34Z","title_canon_sha256":"6c6537a4e586eebce1f05b05e060866c84b91687e39e1a8f01c3231231f12d8e"},"schema_version":"1.0","source":{"id":"1412.7260","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7260","created_at":"2026-05-18T01:20:53Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7260v2","created_at":"2026-05-18T01:20:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7260","created_at":"2026-05-18T01:20:53Z"},{"alias_kind":"pith_short_12","alias_value":"HDHSOC565CXS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HDHSOC565CXSJGAU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HDHSOC56","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b8282b230f7db8537aa5837e40cb412b27880a860495d90d030b6907e1301b9c","target":"graph","created_at":"2026-05-18T01:20:53Z","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":"High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover low-dimensional subspaces and address problems such as clustering, classification, subset selection and more. In this paper, we address the problem of recovering sparse representations for noisy data points in a dictionary whose columns correspond to corrupted data lying close to a union of subspaces. We consider a constrained $\\ell_1$-minimization and study conditions un","authors_text":"Ehsan Elhamifar, Mahdi Soltanolkotabi, Shankar Sastry","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-23T06:10:34Z","title":"Approximate Subspace-Sparse Recovery with Corrupted Data via Constrained $\\ell_1$-Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7260","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":"sha256:0e2cc73e00fa8221a03e38bdb39ff1c13e3822cd04ecd77b61d275e8b2ce9406","target":"record","created_at":"2026-05-18T01:20:53Z","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":"822030c844e395a62201eab8435d49829d0a805e75f272d02ba3da1fffc90289","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2014-12-23T06:10:34Z","title_canon_sha256":"6c6537a4e586eebce1f05b05e060866c84b91687e39e1a8f01c3231231f12d8e"},"schema_version":"1.0","source":{"id":"1412.7260","kind":"arxiv","version":2}},"canonical_sha256":"38cf270bbee8af2498148265dd8a5350c47173ddb4cb85e265cdbd482aef4978","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38cf270bbee8af2498148265dd8a5350c47173ddb4cb85e265cdbd482aef4978","first_computed_at":"2026-05-18T01:20:53.962695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:53.962695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fAOXsiLUWwID9YYAyLs1LBhIz9E3hYx+LBvJX++EO9gi/uApu3VuTskP02eb4FXeqpyyBLekJ3NF1SV7eT6DAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:53.963302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7260","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e2cc73e00fa8221a03e38bdb39ff1c13e3822cd04ecd77b61d275e8b2ce9406","sha256:b8282b230f7db8537aa5837e40cb412b27880a860495d90d030b6907e1301b9c"],"state_sha256":"63e5177b1b07267f5849422fa6d18e85637c543f20f8282679ff6afc058414d4"}