{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:X3G7Z2AUF7IBDAEJIKPZTQDNOP","short_pith_number":"pith:X3G7Z2AU","canonical_record":{"source":{"id":"1507.05532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-07-20T15:23:00Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7fa0cff530ec74d3cc4afb84ca94ce78bf938e864f2c687473ca905aae1dd1e8","abstract_canon_sha256":"8dd4bd9d0cf7dfd7b7ae0421066ed3fea91254b411d73108cb0e51618b86672a"},"schema_version":"1.0"},"canonical_sha256":"becdfce8142fd0118089429f99c06d73dfc2e49eafb6b41004887af4a20a6bb4","source":{"kind":"arxiv","id":"1507.05532","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05532","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05532v2","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05532","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"X3G7Z2AUF7IB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X3G7Z2AUF7IBDAEJ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X3G7Z2AU","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:X3G7Z2AUF7IBDAEJIKPZTQDNOP","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-07-20T15:23:00Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7fa0cff530ec74d3cc4afb84ca94ce78bf938e864f2c687473ca905aae1dd1e8","abstract_canon_sha256":"8dd4bd9d0cf7dfd7b7ae0421066ed3fea91254b411d73108cb0e51618b86672a"},"schema_version":"1.0"},"canonical_sha256":"becdfce8142fd0118089429f99c06d73dfc2e49eafb6b41004887af4a20a6bb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:26.336385Z","signature_b64":"Kq5+XVnUleEMZEesDmHmZ4ITWolnwRcI83cQzZ17U1zpz5LrHOwq/gl6Kn/PIGUi05ztLV4C43MSQ6gfARdJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"becdfce8142fd0118089429f99c06d73dfc2e49eafb6b41004887af4a20a6bb4","last_reissued_at":"2026-05-18T01:33:26.335722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:26.335722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05532","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGjQ/kK6U2en+njFVssNSAkZN0sIm1OpXmmj9WxRrPH1aOpajeUFFE7/DQ5j3W+USQtrBYhvgatYt/9OtPS5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:44:07.717147Z"},"content_sha256":"d282e0da7a993b643fa54e4f794ffb6a0cab05ec200af92d813405a5c0ffe84a","schema_version":"1.0","event_id":"sha256:d282e0da7a993b643fa54e4f794ffb6a0cab05ec200af92d813405a5c0ffe84a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:X3G7Z2AUF7IBDAEJIKPZTQDNOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clustering Tree-structured Data on Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CV","authors_text":"Hongyu Miao, Na Lu","submitted_at":"2015-07-20T15:23:00Z","abstract_excerpt":"Tree-structured data usually contain both topological and geometrical information, and are necessarily considered on manifold instead of Euclidean space for appropriate data parameterization and analysis. In this study, we propose a novel tree-structured data parameterization, called Topology-Attribute matrix (T-A matrix), so the data clustering task can be conducted on matrix manifold. We incorporate the structure constraints embedded in data into the negative matrix factorization method to determine meta-trees from the T-A matrix, and the signature vector of each single tree can then be extr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05532","kind":"arxiv","version":2},"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":"2026-05-18T01:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zo/iDeYW0bZp7UXUxTj/WhYJURL3PcCgYWVnNs84uhihP44dBq/0CGCJEgiCntMWFsybCRYDw2iie5I6ZIT4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:44:07.717799Z"},"content_sha256":"4ac64004c5b4a60adb277263ea10f276dd543ab8341e6ef2e28fd89c5918a2ee","schema_version":"1.0","event_id":"sha256:4ac64004c5b4a60adb277263ea10f276dd543ab8341e6ef2e28fd89c5918a2ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/bundle.json","state_url":"https://pith.science/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/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":"2026-06-08T16:44:07Z","links":{"resolver":"https://pith.science/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP","bundle":"https://pith.science/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/bundle.json","state":"https://pith.science/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X3G7Z2AUF7IBDAEJIKPZTQDNOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X3G7Z2AUF7IBDAEJIKPZTQDNOP","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":"8dd4bd9d0cf7dfd7b7ae0421066ed3fea91254b411d73108cb0e51618b86672a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-07-20T15:23:00Z","title_canon_sha256":"7fa0cff530ec74d3cc4afb84ca94ce78bf938e864f2c687473ca905aae1dd1e8"},"schema_version":"1.0","source":{"id":"1507.05532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05532","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05532v2","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05532","created_at":"2026-05-18T01:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"X3G7Z2AUF7IB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X3G7Z2AUF7IBDAEJ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X3G7Z2AU","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:4ac64004c5b4a60adb277263ea10f276dd543ab8341e6ef2e28fd89c5918a2ee","target":"graph","created_at":"2026-05-18T01:33:26Z","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":"Tree-structured data usually contain both topological and geometrical information, and are necessarily considered on manifold instead of Euclidean space for appropriate data parameterization and analysis. In this study, we propose a novel tree-structured data parameterization, called Topology-Attribute matrix (T-A matrix), so the data clustering task can be conducted on matrix manifold. We incorporate the structure constraints embedded in data into the negative matrix factorization method to determine meta-trees from the T-A matrix, and the signature vector of each single tree can then be extr","authors_text":"Hongyu Miao, Na Lu","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-07-20T15:23:00Z","title":"Clustering Tree-structured Data on Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05532","kind":"arxiv","version":2},"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:d282e0da7a993b643fa54e4f794ffb6a0cab05ec200af92d813405a5c0ffe84a","target":"record","created_at":"2026-05-18T01:33:26Z","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":"8dd4bd9d0cf7dfd7b7ae0421066ed3fea91254b411d73108cb0e51618b86672a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2015-07-20T15:23:00Z","title_canon_sha256":"7fa0cff530ec74d3cc4afb84ca94ce78bf938e864f2c687473ca905aae1dd1e8"},"schema_version":"1.0","source":{"id":"1507.05532","kind":"arxiv","version":2}},"canonical_sha256":"becdfce8142fd0118089429f99c06d73dfc2e49eafb6b41004887af4a20a6bb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"becdfce8142fd0118089429f99c06d73dfc2e49eafb6b41004887af4a20a6bb4","first_computed_at":"2026-05-18T01:33:26.335722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:26.335722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kq5+XVnUleEMZEesDmHmZ4ITWolnwRcI83cQzZ17U1zpz5LrHOwq/gl6Kn/PIGUi05ztLV4C43MSQ6gfARdJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:26.336385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d282e0da7a993b643fa54e4f794ffb6a0cab05ec200af92d813405a5c0ffe84a","sha256:4ac64004c5b4a60adb277263ea10f276dd543ab8341e6ef2e28fd89c5918a2ee"],"state_sha256":"fe0779edc5d064edc1a6584465444fcc0a4ae1ae893be7efa1f5f77dbf4f0109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BhsGMMhhRy1n9w9RDt/4BWhIxSbAT5IwClQsUYDTBSLgLIbk8W3uK/cTlA0f9QlZZP2c0u+BMUticV1mp6ZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:44:07.721767Z","bundle_sha256":"e54c2bdc76619a5c418dc41a0433f4e4419c70f59ca01e0799db0f6df2b6d7b1"}}