{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GRWDC3EHN4ADZDTBLZVF37WL6J","short_pith_number":"pith:GRWDC3EH","schema_version":"1.0","canonical_sha256":"346c316c876f003c8e615e6a5dfecbf244e1281b1a8a812358549b89ba77447f","source":{"kind":"arxiv","id":"1703.07171","version":1},"attestation_state":"computed","paper":{"title":"Non-Convex Rank/Sparsity Regularization and Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carl Olsson, Fredrik Andersson, Marcus Carlsson, Viktor Larsson","submitted_at":"2017-03-21T12:35:01Z","abstract_excerpt":"This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\\ell_1$ or nuclear norm relaxations. It is well known that this approach can be guaranteed to recover a near optimal solutions if a so called restricted isometry property (RIP) holds. On the other hand it is also known to perform soft thresholding which results in a shrinking bias which can degrade the solution.\n  In this paper we study an alternative non-convex regulariza"},"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":"1703.07171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-21T12:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"f267fbfffdfe6156954bfb0318c57470cabbbb909dc6733e5deddbbb7f28af10","abstract_canon_sha256":"7e8bc2efb73ea7938b751cd29ab3179e4c2081885ece670f167f08859c07703f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:11.119009Z","signature_b64":"lJrBJcawHetCoQwzDe7kZXYwW8lc2XBQcihQdU2o8RV9FldNHSOMOg+b7xfsMLdUjEd9AjwJh8nlfNfDvTIBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"346c316c876f003c8e615e6a5dfecbf244e1281b1a8a812358549b89ba77447f","last_reissued_at":"2026-05-18T00:48:11.118433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:11.118433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Convex Rank/Sparsity Regularization and Local Minima","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carl Olsson, Fredrik Andersson, Marcus Carlsson, Viktor Larsson","submitted_at":"2017-03-21T12:35:01Z","abstract_excerpt":"This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\\ell_1$ or nuclear norm relaxations. It is well known that this approach can be guaranteed to recover a near optimal solutions if a so called restricted isometry property (RIP) holds. On the other hand it is also known to perform soft thresholding which results in a shrinking bias which can degrade the solution.\n  In this paper we study an alternative non-convex regulariza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07171","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":""},"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":"1703.07171","created_at":"2026-05-18T00:48:11.118502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.07171v1","created_at":"2026-05-18T00:48:11.118502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07171","created_at":"2026-05-18T00:48:11.118502+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRWDC3EHN4AD","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRWDC3EHN4ADZDTB","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRWDC3EH","created_at":"2026-05-18T12:31:18.294218+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/GRWDC3EHN4ADZDTBLZVF37WL6J","json":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J.json","graph_json":"https://pith.science/api/pith-number/GRWDC3EHN4ADZDTBLZVF37WL6J/graph.json","events_json":"https://pith.science/api/pith-number/GRWDC3EHN4ADZDTBLZVF37WL6J/events.json","paper":"https://pith.science/paper/GRWDC3EH"},"agent_actions":{"view_html":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J","download_json":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J.json","view_paper":"https://pith.science/paper/GRWDC3EH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.07171&json=true","fetch_graph":"https://pith.science/api/pith-number/GRWDC3EHN4ADZDTBLZVF37WL6J/graph.json","fetch_events":"https://pith.science/api/pith-number/GRWDC3EHN4ADZDTBLZVF37WL6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J/action/storage_attestation","attest_author":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J/action/author_attestation","sign_citation":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J/action/citation_signature","submit_replication":"https://pith.science/pith/GRWDC3EHN4ADZDTBLZVF37WL6J/action/replication_record"}},"created_at":"2026-05-18T00:48:11.118502+00:00","updated_at":"2026-05-18T00:48:11.118502+00:00"}