{"doi":"10.17615/xxke-za61","title":"A principal component analysis for trees","abstract":"The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of tree-structured objects. We develop an analog of Principal Component Analysis for trees, based on the notion of tree-lines, and propose numerically fast (linear time) algorithms to solve the resulting optimization problems. The solutions we obtain are used in the analysis of a data set of 73 individuals, where each data object is a tree of blood vessels in one person's brain.","journal":"UNC Libraries","year":2021,"id":211539,"datarank":0.10397207708399181,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"self_citation_contribution":0.10397207708399181,"citation_network_contribution":0.0,"self_endowment_contribution":0.10397207708399181,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9536,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":800976,"name":"Burcu Aydın","orcid":"0000-0001-8456-1320","position":1,"is_corresponding":false},{"id":522492,"name":"J. S. Marron","orcid":"0000-0003-2000-1476","position":2,"is_corresponding":false},{"id":551802,"name":"Haonan Wang","orcid":"0009-0006-6963-8987","position":3,"is_corresponding":false},{"id":197967,"name":"Elizabeth Bullitt","orcid":null,"position":4,"is_corresponding":false},{"id":800975,"name":"Gábor Pataki","orcid":"0000-0001-6377-9806","position":0,"is_corresponding":true}],"reference_count":2,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-07-18T23:52:20.112538Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}