{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZZQ77OXULTIST33JQ7IZYR3YR3","short_pith_number":"pith:ZZQ77OXU","schema_version":"1.0","canonical_sha256":"ce61ffbaf45cd129ef6987d19c47788ec5dcba3e866091c59133104b69fbaaa2","source":{"kind":"arxiv","id":"1306.2194","version":1},"attestation_state":"computed","paper":{"title":"Adaptive Noisy Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Michael Chichignoud, S\\'ebastien Loustau","submitted_at":"2013-06-10T13:15:25Z","abstract_excerpt":"The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular {\\it $k$-means} is not suitable in this case. In this paper, we propose a noisy $k$-means minimization, which is based on the $k$-means loss function and a deconvolution estimator of the density $f$. In particular, this approach suffers from the dependence on a bandwidth i"},"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":"1306.2194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-06-10T13:15:25Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"a198aae45dc4543e359bbaed9efa9d0419235445ae2674d9d3fe7484d79d98b9","abstract_canon_sha256":"a783fc359bca94928c86b8b4e8bf36d1dfc3c9c0403692851bf4ab7a248179b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:22.088597Z","signature_b64":"hueeXixUe/qcd5gtFcbpaTVCc/8k9ahoUqGIxUMTovTSpjmde7j6EoI9I42AyTQ8iAEwBdeYRjeU9A3Yk4ZXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce61ffbaf45cd129ef6987d19c47788ec5dcba3e866091c59133104b69fbaaa2","last_reissued_at":"2026-05-18T03:21:22.088189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:22.088189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adaptive Noisy Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Michael Chichignoud, S\\'ebastien Loustau","submitted_at":"2013-06-10T13:15:25Z","abstract_excerpt":"The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the Lebesgue measure. Since we observe a corrupted sample, a direct approach as the popular {\\it $k$-means} is not suitable in this case. In this paper, we propose a noisy $k$-means minimization, which is based on the $k$-means loss function and a deconvolution estimator of the density $f$. In particular, this approach suffers from the dependence on a bandwidth i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2194","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":"1306.2194","created_at":"2026-05-18T03:21:22.088251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.2194v1","created_at":"2026-05-18T03:21:22.088251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2194","created_at":"2026-05-18T03:21:22.088251+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZZQ77OXULTIS","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZZQ77OXULTIST33J","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZZQ77OXU","created_at":"2026-05-18T12:28:09.283467+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/ZZQ77OXULTIST33JQ7IZYR3YR3","json":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3.json","graph_json":"https://pith.science/api/pith-number/ZZQ77OXULTIST33JQ7IZYR3YR3/graph.json","events_json":"https://pith.science/api/pith-number/ZZQ77OXULTIST33JQ7IZYR3YR3/events.json","paper":"https://pith.science/paper/ZZQ77OXU"},"agent_actions":{"view_html":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3","download_json":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3.json","view_paper":"https://pith.science/paper/ZZQ77OXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.2194&json=true","fetch_graph":"https://pith.science/api/pith-number/ZZQ77OXULTIST33JQ7IZYR3YR3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZZQ77OXULTIST33JQ7IZYR3YR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3/action/storage_attestation","attest_author":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3/action/author_attestation","sign_citation":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3/action/citation_signature","submit_replication":"https://pith.science/pith/ZZQ77OXULTIST33JQ7IZYR3YR3/action/replication_record"}},"created_at":"2026-05-18T03:21:22.088251+00:00","updated_at":"2026-05-18T03:21:22.088251+00:00"}