{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IYVWILX2OYJLBCTGYBL2W55MJX","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":"238f3f8dcb22ad7acc9382a62f8c5ad9c6bc07182825899cf312779ac445fe9d","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-08T03:09:13Z","title_canon_sha256":"04e887579510bf9a10cb59715e117f72400811ae815a28c31175b072587623ee"},"schema_version":"1.0","source":{"id":"1510.02189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02189","created_at":"2026-05-18T01:11:46Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02189v2","created_at":"2026-05-18T01:11:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02189","created_at":"2026-05-18T01:11:46Z"},{"alias_kind":"pith_short_12","alias_value":"IYVWILX2OYJL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"IYVWILX2OYJLBCTG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"IYVWILX2","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:60a543682951048853e926f0251056d6beb61a872ce6ba04514020a38a442ff7","target":"graph","created_at":"2026-05-18T01:11:46Z","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 discuss a strategy of sparse approximation that is based on the use of an overcomplete basis, and evaluate its performance when a random matrix is used as this basis. A small combination of basis vectors is chosen from a given overcomplete basis, according to a given compression rate, such that they compactly represent the target data with as small a distortion as possible. As a selection method, we study the $\\ell_0$- and $\\ell_1$-based methods, which employ the exhaustive search and $\\ell_1$-norm regularization techniques, respectively. The performance is assessed in terms of the trade-of","authors_text":"Masato Okada, Tomoyuki Obuchi, Yoshinori Nakanishi-Ohno, Yoshiyuki Kabashima","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-08T03:09:13Z","title":"Sparse approximation based on a random overcomplete basis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02189","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":"sha256:1a64511a0b49cadf6d38d2fb474a1b44325d7f50093aa7accb6618c1795a143a","target":"record","created_at":"2026-05-18T01:11:46Z","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":"238f3f8dcb22ad7acc9382a62f8c5ad9c6bc07182825899cf312779ac445fe9d","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-08T03:09:13Z","title_canon_sha256":"04e887579510bf9a10cb59715e117f72400811ae815a28c31175b072587623ee"},"schema_version":"1.0","source":{"id":"1510.02189","kind":"arxiv","version":2}},"canonical_sha256":"462b642efa7612b08a66c057ab77ac4dc61576a64c1dcd1a2b2027eef31ea24f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"462b642efa7612b08a66c057ab77ac4dc61576a64c1dcd1a2b2027eef31ea24f","first_computed_at":"2026-05-18T01:11:46.639986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:46.639986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sq1EY7kwZLrELkrwo3z7rNVy1WBYKOO13BoY6Vu7L6vYQOihNcbiwfMoLqUVJY107zA0bDNklulC7ZORVjJZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:46.640368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a64511a0b49cadf6d38d2fb474a1b44325d7f50093aa7accb6618c1795a143a","sha256:60a543682951048853e926f0251056d6beb61a872ce6ba04514020a38a442ff7"],"state_sha256":"83827a243109ef5d7744cc4cb3cff3ffe1b7d09be2c843efcb978e11f9366f6b"}