{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XI2PPOT7P4S5CYN3RLV7OKDP5C","short_pith_number":"pith:XI2PPOT7","schema_version":"1.0","canonical_sha256":"ba34f7ba7f7f25d161bb8aebf7286fe8ad3366c7d595c39aae2d8fd837469af6","source":{"kind":"arxiv","id":"1807.05241","version":1},"attestation_state":"computed","paper":{"title":"Approximation Algorithms for Clustering via Weighted Impurity Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Eduardo Laber, Ferdinando Cicalese","submitted_at":"2018-07-13T18:14:11Z","abstract_excerpt":"An impurity measures $I:{R}^k \\to {R}^+$ maps a $k$-dimensional vector ${\\bf v}$ to a non-negative value $I({\\bf v})$ so that the more homogeneous ${\\bf v}$, the larger its impurity. We study clustering based on impurity measures: given a collection $V$ of $n$ many $k$-dimensional vectors and an impurity measure $I$, the goal is to find a partition ${\\cal P}$ of $V$ into $L$ groups $V_1,\\ldots,V_L$ that minimizes the total impurities of the groups in ${\\cal P}$, i.e., $I({\\cal P})= \\sum_{m=1}^{L} I(\\sum_{{\\bf v} \\in V_m}{\\bf v}).$\n  Impurity minimization is widely used as quality assessment me"},"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":"1807.05241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-13T18:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"f78737c7df18098e3cb37400ca924008fdb24ba762ec1aab4154c22bbf06c742","abstract_canon_sha256":"a9280c4101e6b80e998566aebe7e184e7784dc30c0ab264f13b2230a7b5d0a91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:44.037768Z","signature_b64":"BSO4tA604RW3WzQz8F4nE70Tww/GNudjCLvPDmqP/wJRQ8rCJvCKl91HwYBeHc2LdDk14RNgIboyOm9Hk26/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba34f7ba7f7f25d161bb8aebf7286fe8ad3366c7d595c39aae2d8fd837469af6","last_reissued_at":"2026-05-18T00:10:44.037296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:44.037296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation Algorithms for Clustering via Weighted Impurity Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Eduardo Laber, Ferdinando Cicalese","submitted_at":"2018-07-13T18:14:11Z","abstract_excerpt":"An impurity measures $I:{R}^k \\to {R}^+$ maps a $k$-dimensional vector ${\\bf v}$ to a non-negative value $I({\\bf v})$ so that the more homogeneous ${\\bf v}$, the larger its impurity. We study clustering based on impurity measures: given a collection $V$ of $n$ many $k$-dimensional vectors and an impurity measure $I$, the goal is to find a partition ${\\cal P}$ of $V$ into $L$ groups $V_1,\\ldots,V_L$ that minimizes the total impurities of the groups in ${\\cal P}$, i.e., $I({\\cal P})= \\sum_{m=1}^{L} I(\\sum_{{\\bf v} \\in V_m}{\\bf v}).$\n  Impurity minimization is widely used as quality assessment me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05241","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":"1807.05241","created_at":"2026-05-18T00:10:44.037382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.05241v1","created_at":"2026-05-18T00:10:44.037382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05241","created_at":"2026-05-18T00:10:44.037382+00:00"},{"alias_kind":"pith_short_12","alias_value":"XI2PPOT7P4S5","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XI2PPOT7P4S5CYN3","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XI2PPOT7","created_at":"2026-05-18T12:33:01.666342+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/XI2PPOT7P4S5CYN3RLV7OKDP5C","json":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C.json","graph_json":"https://pith.science/api/pith-number/XI2PPOT7P4S5CYN3RLV7OKDP5C/graph.json","events_json":"https://pith.science/api/pith-number/XI2PPOT7P4S5CYN3RLV7OKDP5C/events.json","paper":"https://pith.science/paper/XI2PPOT7"},"agent_actions":{"view_html":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C","download_json":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C.json","view_paper":"https://pith.science/paper/XI2PPOT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.05241&json=true","fetch_graph":"https://pith.science/api/pith-number/XI2PPOT7P4S5CYN3RLV7OKDP5C/graph.json","fetch_events":"https://pith.science/api/pith-number/XI2PPOT7P4S5CYN3RLV7OKDP5C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C/action/storage_attestation","attest_author":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C/action/author_attestation","sign_citation":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C/action/citation_signature","submit_replication":"https://pith.science/pith/XI2PPOT7P4S5CYN3RLV7OKDP5C/action/replication_record"}},"created_at":"2026-05-18T00:10:44.037382+00:00","updated_at":"2026-05-18T00:10:44.037382+00:00"}