{"doi":"10.1007/s10994-021-05953-4","title":"Efficient Weingarten map and curvature estimation on manifolds","abstract":null,"journal":"Machine Learning","year":2021,"id":634853,"datarank":0.3958585994422889,"base_score":2.639057329615259,"endowment":2.639057329615259,"self_citation_contribution":0.3958585994422889,"citation_network_contribution":0.0,"self_endowment_contribution":0.3958585994422889,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":13,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":796441,"name":"Didong Li","orcid":"0000-0001-9146-705X","position":1,"is_corresponding":false},{"id":1646773,"name":"Huafei Sun","orcid":null,"position":2,"is_corresponding":false},{"id":1646774,"name":"Amir H. Assadi","orcid":null,"position":3,"is_corresponding":false},{"id":1646775,"name":"Shiqiang Zhang","orcid":null,"position":4,"is_corresponding":false},{"id":1646772,"name":"Yueqi Cao","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"resolved":true,"title":"Efficient Weingarten map and curvature estimation on manifolds","abstract":"In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. We verify the convergence rate through simulated data and apply the estimated Weingarten map to curvature estimation and point cloud simplification to multiple real data sets.","is_dataset_classified":null,"base_score":2.5649493574615367,"endowment":2.5649493574615367,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"19767382","pmcid":null,"openalex_id":"https://openalex.org/W3083584047","authors":[],"funders":[],"total_grants":0,"fwci":2.4189,"citation_percentile":0.87918436,"influential_citations":0,"citation_trend":[{"year":2021,"count":1},{"year":2022,"count":3},{"year":2024,"count":2},{"year":2025,"count":4},{"year":2026,"count":2}],"oa_status":"hybrid","license":"other-oa","oa_locations":[{"url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05953-4.pdf","host_type":"journal"},{"url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05953-4.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1007/s10994-021-05953-4","host_type":"journal"},{"url":"http://arxiv.org/abs/1905.10725","host_type":"repository"},{"url":"https://arxiv.org/pdf/1905.10725","host_type":"repository"}],"fields_of_study":["Morphological variations and asymmetry","Point processes and geometric inequalities","Statistical Methods and Inference"],"mesh_terms":[],"keywords":["Point cloud","Curvature","Rate of convergence","Manifold (fluid mechanics)","Convergence (economics)","Euclidean geometry","Property (philosophy)","Estimation"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-08-06T14:16:21.311260Z","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":[]}