{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UNWMAHYK2B3LNYW243SBKAWENS","short_pith_number":"pith:UNWMAHYK","canonical_record":{"source":{"id":"1611.01408","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-11-04T15:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"ea6bb13b19db77a2745437f8268c8214288b6f2e02628124717b149e87307481","abstract_canon_sha256":"017d83caf66c9cae303199124e21e2ca6f58b17b9a81a36826cd3fa9b46eec86"},"schema_version":"1.0"},"canonical_sha256":"a36cc01f0ad076b6e2dae6e41502c46cb9dca800adfbf0f3e935882619082148","source":{"kind":"arxiv","id":"1611.01408","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01408","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01408v5","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01408","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"UNWMAHYK2B3L","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNWMAHYK2B3LNYW2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNWMAHYK","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UNWMAHYK2B3LNYW243SBKAWENS","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01408","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-11-04T15:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"ea6bb13b19db77a2745437f8268c8214288b6f2e02628124717b149e87307481","abstract_canon_sha256":"017d83caf66c9cae303199124e21e2ca6f58b17b9a81a36826cd3fa9b46eec86"},"schema_version":"1.0"},"canonical_sha256":"a36cc01f0ad076b6e2dae6e41502c46cb9dca800adfbf0f3e935882619082148","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:48.879898Z","signature_b64":"lfIrztJ/74isjxoKKy1Jb+59AU4bBeEvESFPwxXf/yVrjIcinq3HqhMCiZkOaF5s63lL4iLUqZvM2EUjLeNyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a36cc01f0ad076b6e2dae6e41502c46cb9dca800adfbf0f3e935882619082148","last_reissued_at":"2026-05-18T00:46:48.879237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:48.879237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01408","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eLLej9xUTa4UUsxij9QFFDeVZ3IzHcHetieBoqJB/4yimuHflZG1mhr6gGiXRw/qDSUXVBncT/t7cZcvYn61BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:21:33.194806Z"},"content_sha256":"6cdc43d1e85130fd84e855cfae35cffa96999838d7e9c2566ac154a57e901445","schema_version":"1.0","event_id":"sha256:6cdc43d1e85130fd84e855cfae35cffa96999838d7e9c2566ac154a57e901445"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UNWMAHYK2B3LNYW243SBKAWENS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Guillermo Sapiro, Mariano Tepper","submitted_at":"2016-11-04T15:09:24Z","abstract_excerpt":"In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01408","kind":"arxiv","version":5},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q91ptC1KpDPFEb91HhEerVY50XwIBGGDpMsZu92klJFY3VwPyhbFYIAviVzQSn4IfMoURV/PB1RPJb2kxzyVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:21:33.195298Z"},"content_sha256":"b249fddfccb1e426279d1ff73d43a5951611556c12c4c94c1536414ee6d73e46","schema_version":"1.0","event_id":"sha256:b249fddfccb1e426279d1ff73d43a5951611556c12c4c94c1536414ee6d73e46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNWMAHYK2B3LNYW243SBKAWENS/bundle.json","state_url":"https://pith.science/pith/UNWMAHYK2B3LNYW243SBKAWENS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNWMAHYK2B3LNYW243SBKAWENS/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":"2026-05-30T18:21:33Z","links":{"resolver":"https://pith.science/pith/UNWMAHYK2B3LNYW243SBKAWENS","bundle":"https://pith.science/pith/UNWMAHYK2B3LNYW243SBKAWENS/bundle.json","state":"https://pith.science/pith/UNWMAHYK2B3LNYW243SBKAWENS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNWMAHYK2B3LNYW243SBKAWENS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UNWMAHYK2B3LNYW243SBKAWENS","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":"017d83caf66c9cae303199124e21e2ca6f58b17b9a81a36826cd3fa9b46eec86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-11-04T15:09:24Z","title_canon_sha256":"ea6bb13b19db77a2745437f8268c8214288b6f2e02628124717b149e87307481"},"schema_version":"1.0","source":{"id":"1611.01408","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01408","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01408v5","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01408","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"UNWMAHYK2B3L","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UNWMAHYK2B3LNYW2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UNWMAHYK","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b249fddfccb1e426279d1ff73d43a5951611556c12c4c94c1536414ee6d73e46","target":"graph","created_at":"2026-05-18T00:46:48Z","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":"In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers s","authors_text":"Guillermo Sapiro, Mariano Tepper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-11-04T15:09:24Z","title":"Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01408","kind":"arxiv","version":5},"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":"sha256:6cdc43d1e85130fd84e855cfae35cffa96999838d7e9c2566ac154a57e901445","target":"record","created_at":"2026-05-18T00:46:48Z","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":"017d83caf66c9cae303199124e21e2ca6f58b17b9a81a36826cd3fa9b46eec86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-11-04T15:09:24Z","title_canon_sha256":"ea6bb13b19db77a2745437f8268c8214288b6f2e02628124717b149e87307481"},"schema_version":"1.0","source":{"id":"1611.01408","kind":"arxiv","version":5}},"canonical_sha256":"a36cc01f0ad076b6e2dae6e41502c46cb9dca800adfbf0f3e935882619082148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a36cc01f0ad076b6e2dae6e41502c46cb9dca800adfbf0f3e935882619082148","first_computed_at":"2026-05-18T00:46:48.879237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:48.879237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lfIrztJ/74isjxoKKy1Jb+59AU4bBeEvESFPwxXf/yVrjIcinq3HqhMCiZkOaF5s63lL4iLUqZvM2EUjLeNyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:48.879898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01408","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cdc43d1e85130fd84e855cfae35cffa96999838d7e9c2566ac154a57e901445","sha256:b249fddfccb1e426279d1ff73d43a5951611556c12c4c94c1536414ee6d73e46"],"state_sha256":"2df512b354cef1530d57f03a3f196423abc489af4a872e1b76130fd652bd5aeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fsz3Sc48Bnx+5KZekd/M5BMCjLQuSfjyWyFqoRcvC2q0Ba3eApz4AdydT6dC25NXgW9TlqtZDPWUtACg6GinCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:21:33.198201Z","bundle_sha256":"e981e02b3e405bd3007c644ac139ad694e5976a6c29b5a6bc21ddd58d634c435"}}