{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UILUQOZBYPUWKS7ANIVF77VXY4","short_pith_number":"pith:UILUQOZB","schema_version":"1.0","canonical_sha256":"a217483b21c3e9654be06a2a5ffeb7c72c6f87c9cfa7728c47798dd44c4f8c62","source":{"kind":"arxiv","id":"1603.01775","version":2},"attestation_state":"computed","paper":{"title":"Combined Analysis of Amplitude and Phase Variations in Functional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Sungkyu Jung, Sungwon Lee","submitted_at":"2016-03-06T01:47:56Z","abstract_excerpt":"When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A downside of this approach is that the important variations contained in the phases are completely ignored. To combine both of amplitude and phase variations, we propose a variant of principal component analysis (PCA) that captures non-linear components representing the amplitude, phase and their associations simultaneously. The proposed method, which we call fu"},"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":"1603.01775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-03-06T01:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"6d5829171f9d373b1b374bdf40aeb851418474f547459ffdddf1705dfb30a458","abstract_canon_sha256":"8ea4d9366f909c4105e0b98717f634cab0b2b2b013f93aa7d4d72497bc98dada"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:35.885912Z","signature_b64":"9eWuhiu6+hHOB28kgJvWOWG2oeEZo9IaaK/jeAPTALknYA40kKRqngMU0z+e8C/KeeiFiQM0Cr2VWdjIXOIvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a217483b21c3e9654be06a2a5ffeb7c72c6f87c9cfa7728c47798dd44c4f8c62","last_reissued_at":"2026-05-18T00:43:35.885428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:35.885428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combined Analysis of Amplitude and Phase Variations in Functional Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Sungkyu Jung, Sungwon Lee","submitted_at":"2016-03-06T01:47:56Z","abstract_excerpt":"When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A downside of this approach is that the important variations contained in the phases are completely ignored. To combine both of amplitude and phase variations, we propose a variant of principal component analysis (PCA) that captures non-linear components representing the amplitude, phase and their associations simultaneously. The proposed method, which we call fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01775","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":"1603.01775","created_at":"2026-05-18T00:43:35.885496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01775v2","created_at":"2026-05-18T00:43:35.885496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01775","created_at":"2026-05-18T00:43:35.885496+00:00"},{"alias_kind":"pith_short_12","alias_value":"UILUQOZBYPUW","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UILUQOZBYPUWKS7A","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UILUQOZB","created_at":"2026-05-18T12:30:46.583412+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/UILUQOZBYPUWKS7ANIVF77VXY4","json":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4.json","graph_json":"https://pith.science/api/pith-number/UILUQOZBYPUWKS7ANIVF77VXY4/graph.json","events_json":"https://pith.science/api/pith-number/UILUQOZBYPUWKS7ANIVF77VXY4/events.json","paper":"https://pith.science/paper/UILUQOZB"},"agent_actions":{"view_html":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4","download_json":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4.json","view_paper":"https://pith.science/paper/UILUQOZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01775&json=true","fetch_graph":"https://pith.science/api/pith-number/UILUQOZBYPUWKS7ANIVF77VXY4/graph.json","fetch_events":"https://pith.science/api/pith-number/UILUQOZBYPUWKS7ANIVF77VXY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4/action/storage_attestation","attest_author":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4/action/author_attestation","sign_citation":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4/action/citation_signature","submit_replication":"https://pith.science/pith/UILUQOZBYPUWKS7ANIVF77VXY4/action/replication_record"}},"created_at":"2026-05-18T00:43:35.885496+00:00","updated_at":"2026-05-18T00:43:35.885496+00:00"}