{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OACBL5IC5JYQLCTZNFI3V6SMYL","short_pith_number":"pith:OACBL5IC","canonical_record":{"source":{"id":"1011.4321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-11-18T22:20:45Z","cross_cats_sorted":[],"title_canon_sha256":"6200d6ba2f9c3368e6c90a8dbf4801311e73752b0c8f3e1ebd583c758a4c89a8","abstract_canon_sha256":"b62093944c657ba69f1c03f6ead4e87c15a55968b0dfcad83dccd1205b39d4ce"},"schema_version":"1.0"},"canonical_sha256":"700415f502ea71058a796951bafa4cc2e6ed78bee3a1bb3204845e98a1d2e1cc","source":{"kind":"arxiv","id":"1011.4321","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4321","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4321v1","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4321","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"OACBL5IC5JYQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OACBL5IC5JYQLCTZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OACBL5IC","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OACBL5IC5JYQLCTZNFI3V6SMYL","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-11-18T22:20:45Z","cross_cats_sorted":[],"title_canon_sha256":"6200d6ba2f9c3368e6c90a8dbf4801311e73752b0c8f3e1ebd583c758a4c89a8","abstract_canon_sha256":"b62093944c657ba69f1c03f6ead4e87c15a55968b0dfcad83dccd1205b39d4ce"},"schema_version":"1.0"},"canonical_sha256":"700415f502ea71058a796951bafa4cc2e6ed78bee3a1bb3204845e98a1d2e1cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:36.227643Z","signature_b64":"B714J6gKxpRmn9Fo10q4O2cR2KlTtWnnCANDVzCioyR3i2PmelTM7kkO3qBNV2sAI/a9T3h9dEOTJiSWWLaMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"700415f502ea71058a796951bafa4cc2e6ed78bee3a1bb3204845e98a1d2e1cc","last_reissued_at":"2026-05-18T02:23:36.226928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:36.226928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4321","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nV6Smsv7fG0wIh/g8oY1TEZ/hlXoXfz0VHwrF5oQYi+kKvonHgzWhrdFhE2sdmlLJQzDsqYer3Gq++PptzUMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T09:46:28.691374Z"},"content_sha256":"63f8b0f7b6e5f2e8566fefa41f4c3c29ad4b3d39b6155ce95bbc5fb863c70b79","schema_version":"1.0","event_id":"sha256:63f8b0f7b6e5f2e8566fefa41f4c3c29ad4b3d39b6155ce95bbc5fb863c70b79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OACBL5IC5JYQLCTZNFI3V6SMYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Fuzzy Clustering Model for Fuzzy Data with Outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"M.H.Fazel Zarandi, Zahra S. Razaee","submitted_at":"2010-11-18T22:20:45Z","abstract_excerpt":"In this paper a fuzzy clustering model for fuzzy data with outliers is proposed. The model is based on Wasserstein distance between interval valued data which is generalized to fuzzy data. In addition, Keller's approach is used to identify outliers and reduce their influences. We have also defined a transformation to change our distance to the Euclidean distance. With the help of this approach, the problem of fuzzy clustering of fuzzy data is reduced to fuzzy clustering of crisp data. In order to show the performance of the proposed clustering algorithm, two simulation experiments are discusse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4321","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6srLUn3KWA06RCtJFYDnZAu2uoFtSS4VSRYI31ZHzdjoVRa08at+x4eyqnxU/8MpR5Rt2oivm+0fzXPcpKJMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-19T09:46:28.691720Z"},"content_sha256":"4f8dc851a2fed36ebc6c990dd5646c2b12aa8ef4892b2f97bde81aba16e0f2ed","schema_version":"1.0","event_id":"sha256:4f8dc851a2fed36ebc6c990dd5646c2b12aa8ef4892b2f97bde81aba16e0f2ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/bundle.json","state_url":"https://pith.science/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/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":"2026-07-19T09:46:28Z","links":{"resolver":"https://pith.science/pith/OACBL5IC5JYQLCTZNFI3V6SMYL","bundle":"https://pith.science/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/bundle.json","state":"https://pith.science/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OACBL5IC5JYQLCTZNFI3V6SMYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OACBL5IC5JYQLCTZNFI3V6SMYL","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":"b62093944c657ba69f1c03f6ead4e87c15a55968b0dfcad83dccd1205b39d4ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-11-18T22:20:45Z","title_canon_sha256":"6200d6ba2f9c3368e6c90a8dbf4801311e73752b0c8f3e1ebd583c758a4c89a8"},"schema_version":"1.0","source":{"id":"1011.4321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4321","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4321v1","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4321","created_at":"2026-05-18T02:23:36Z"},{"alias_kind":"pith_short_12","alias_value":"OACBL5IC5JYQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OACBL5IC5JYQLCTZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OACBL5IC","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:4f8dc851a2fed36ebc6c990dd5646c2b12aa8ef4892b2f97bde81aba16e0f2ed","target":"graph","created_at":"2026-05-18T02:23:36Z","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 paper a fuzzy clustering model for fuzzy data with outliers is proposed. The model is based on Wasserstein distance between interval valued data which is generalized to fuzzy data. In addition, Keller's approach is used to identify outliers and reduce their influences. We have also defined a transformation to change our distance to the Euclidean distance. With the help of this approach, the problem of fuzzy clustering of fuzzy data is reduced to fuzzy clustering of crisp data. In order to show the performance of the proposed clustering algorithm, two simulation experiments are discusse","authors_text":"M.H.Fazel Zarandi, Zahra S. Razaee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-11-18T22:20:45Z","title":"A Fuzzy Clustering Model for Fuzzy Data with Outliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4321","kind":"arxiv","version":1},"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":"sha256:63f8b0f7b6e5f2e8566fefa41f4c3c29ad4b3d39b6155ce95bbc5fb863c70b79","target":"record","created_at":"2026-05-18T02:23:36Z","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":"b62093944c657ba69f1c03f6ead4e87c15a55968b0dfcad83dccd1205b39d4ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2010-11-18T22:20:45Z","title_canon_sha256":"6200d6ba2f9c3368e6c90a8dbf4801311e73752b0c8f3e1ebd583c758a4c89a8"},"schema_version":"1.0","source":{"id":"1011.4321","kind":"arxiv","version":1}},"canonical_sha256":"700415f502ea71058a796951bafa4cc2e6ed78bee3a1bb3204845e98a1d2e1cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"700415f502ea71058a796951bafa4cc2e6ed78bee3a1bb3204845e98a1d2e1cc","first_computed_at":"2026-05-18T02:23:36.226928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:36.226928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B714J6gKxpRmn9Fo10q4O2cR2KlTtWnnCANDVzCioyR3i2PmelTM7kkO3qBNV2sAI/a9T3h9dEOTJiSWWLaMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:36.227643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63f8b0f7b6e5f2e8566fefa41f4c3c29ad4b3d39b6155ce95bbc5fb863c70b79","sha256:4f8dc851a2fed36ebc6c990dd5646c2b12aa8ef4892b2f97bde81aba16e0f2ed"],"state_sha256":"8fae5015b60abd86a95153238219267ad653b359a6225314ea61426391397e14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQbK+g0femTwXCHf5wLB3YaomYyaabpOmkinBH9V1BxEiaV4p6hrsN/9Y/ZjuZLMBG9nabX9wNfx4UXs7u7DDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-19T09:46:28.694204Z","bundle_sha256":"a2419b2fc3a00846933834120a42234eaf67bdcdfb86cabc93207f7ff6a1e8f4"}}