{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4JZH45HC5K7TLI6PAV2IC7SUQL","short_pith_number":"pith:4JZH45HC","schema_version":"1.0","canonical_sha256":"e2727e74e2eabf35a3cf0574817e5482e94cea26fbcb6a5098ae640f43de18ce","source":{"kind":"arxiv","id":"1601.01741","version":2},"attestation_state":"computed","paper":{"title":"Persistence weighted Gaussian kernel for topological data analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Genki Kusano, Kenji Fukumizu, Yasuaki Hiraoka","submitted_at":"2016-01-08T01:29:28Z","abstract_excerpt":"Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide gl"},"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":"1601.01741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-01-08T01:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"5c3cbaac8ecd8f5b8a4226869b00a337791e90d616fe3d9114608deb67a5acea","abstract_canon_sha256":"f8b73a15da933c56f8aecdef48f96fd3bfc076e6adabdc48a45cc5f02b316027"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:14.854074Z","signature_b64":"Ry5toUcRv3LjXukpRQUjwiJbKxjAPajmkUrquv1BAZoj/kVnukIybV9STCc2eRX1yGvIUYlwnUOEaVZfzpnnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2727e74e2eabf35a3cf0574817e5482e94cea26fbcb6a5098ae640f43de18ce","last_reissued_at":"2026-05-18T01:16:14.853278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:14.853278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Persistence weighted Gaussian kernel for topological data analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Genki Kusano, Kenji Fukumizu, Yasuaki Hiraoka","submitted_at":"2016-01-08T01:29:28Z","abstract_excerpt":"Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persistence diagrams to develop a statistical framework in TDA. The proposed kernel satisfies the stability property and provides explicit control on the effect of persistence. Furthermore, the method allows a fast approximation technique. The method is applied into practical data on proteins and oxide gl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01741","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.01741","created_at":"2026-05-18T01:16:14.853421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.01741v2","created_at":"2026-05-18T01:16:14.853421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.01741","created_at":"2026-05-18T01:16:14.853421+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JZH45HC5K7T","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JZH45HC5K7TLI6P","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JZH45HC","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.16957","citing_title":"On the Spectral Synthesis of Lipschitz Persistence Diagram Vectorizations","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL","json":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL.json","graph_json":"https://pith.science/api/pith-number/4JZH45HC5K7TLI6PAV2IC7SUQL/graph.json","events_json":"https://pith.science/api/pith-number/4JZH45HC5K7TLI6PAV2IC7SUQL/events.json","paper":"https://pith.science/paper/4JZH45HC"},"agent_actions":{"view_html":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL","download_json":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL.json","view_paper":"https://pith.science/paper/4JZH45HC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.01741&json=true","fetch_graph":"https://pith.science/api/pith-number/4JZH45HC5K7TLI6PAV2IC7SUQL/graph.json","fetch_events":"https://pith.science/api/pith-number/4JZH45HC5K7TLI6PAV2IC7SUQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL/action/storage_attestation","attest_author":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL/action/author_attestation","sign_citation":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL/action/citation_signature","submit_replication":"https://pith.science/pith/4JZH45HC5K7TLI6PAV2IC7SUQL/action/replication_record"}},"created_at":"2026-05-18T01:16:14.853421+00:00","updated_at":"2026-05-18T01:16:14.853421+00:00"}