{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VJL5I3GBR4ILJGMXM7L2HGV7BM","short_pith_number":"pith:VJL5I3GB","schema_version":"1.0","canonical_sha256":"aa57d46cc18f10b4999767d7a39abf0b3a9ca536405775699bf0ea108ce8ecff","source":{"kind":"arxiv","id":"1503.07027","version":4},"attestation_state":"computed","paper":{"title":"Convergence radius and sample complexity of ITKM algorithms for dictionary learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Karin Schnass","submitted_at":"2015-03-24T13:29:12Z","abstract_excerpt":"In this work we show that iterative thresholding and K-means (ITKM) algorithms can recover a generating dictionary with K atoms from noisy $S$ sparse signals up to an error $\\tilde \\varepsilon$ as long as the initialisation is within a convergence radius, that is up to a $\\log K$ factor inversely proportional to the dynamic range of the signals, and the sample size is proportional to $K \\log K \\tilde \\varepsilon^{-2}$. The results are valid for arbitrary target errors if the sparsity level is of the order of the square root of the signal dimension $d$ and for target errors down to $K^{-\\ell}$ "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.07027","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-03-24T13:29:12Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"66b2fc245080f5fab987c935e90506f3e2c045329a0f15a59f04814892ee2d4f","abstract_canon_sha256":"00a616501ba39ec5d023846027bec04063b6d3adaf389f8ede7b59794c15bdb9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:42.251602Z","signature_b64":"Za8EbvNMiHJKK05MVTwHA1IOmE+NQ9n/aSIa7DALTV1vHG4nfA5tngS/JjE7R3+OY0qbhCZ0fXjkGQKoXb17Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa57d46cc18f10b4999767d7a39abf0b3a9ca536405775699bf0ea108ce8ecff","last_reissued_at":"2026-05-18T01:09:42.251111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:42.251111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence radius and sample complexity of ITKM algorithms for dictionary learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Karin Schnass","submitted_at":"2015-03-24T13:29:12Z","abstract_excerpt":"In this work we show that iterative thresholding and K-means (ITKM) algorithms can recover a generating dictionary with K atoms from noisy $S$ sparse signals up to an error $\\tilde \\varepsilon$ as long as the initialisation is within a convergence radius, that is up to a $\\log K$ factor inversely proportional to the dynamic range of the signals, and the sample size is proportional to $K \\log K \\tilde \\varepsilon^{-2}$. The results are valid for arbitrary target errors if the sparsity level is of the order of the square root of the signal dimension $d$ and for target errors down to $K^{-\\ell}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07027","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.07027","created_at":"2026-05-18T01:09:42.251196+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.07027v4","created_at":"2026-05-18T01:09:42.251196+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07027","created_at":"2026-05-18T01:09:42.251196+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJL5I3GBR4IL","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJL5I3GBR4ILJGMX","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJL5I3GB","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM","json":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM.json","graph_json":"https://pith.science/api/pith-number/VJL5I3GBR4ILJGMXM7L2HGV7BM/graph.json","events_json":"https://pith.science/api/pith-number/VJL5I3GBR4ILJGMXM7L2HGV7BM/events.json","paper":"https://pith.science/paper/VJL5I3GB"},"agent_actions":{"view_html":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM","download_json":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM.json","view_paper":"https://pith.science/paper/VJL5I3GB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.07027&json=true","fetch_graph":"https://pith.science/api/pith-number/VJL5I3GBR4ILJGMXM7L2HGV7BM/graph.json","fetch_events":"https://pith.science/api/pith-number/VJL5I3GBR4ILJGMXM7L2HGV7BM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM/action/storage_attestation","attest_author":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM/action/author_attestation","sign_citation":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM/action/citation_signature","submit_replication":"https://pith.science/pith/VJL5I3GBR4ILJGMXM7L2HGV7BM/action/replication_record"}},"created_at":"2026-05-18T01:09:42.251196+00:00","updated_at":"2026-05-18T01:09:42.251196+00:00"}