{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T01:49:49Z","timestamp":1763171389620,"version":"3.45.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T00:00:00Z","timestamp":1742169600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T00:00:00Z","timestamp":1742169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004663","name":"the Ministry of Science and Technology of Taiwan","doi-asserted-by":"crossref","award":["MOST102-2118-M-029-005"],"award-info":[{"award-number":["MOST102-2118-M-029-005"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Classif"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s00357-025-09503-8","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T00:51:02Z","timestamp":1742172662000},"page":"565-595","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Curve Clustering via Pairwise Directions Estimation"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0045-470X","authenticated-orcid":false,"given":"Heng-Hui","family":"Lue","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,17]]},"reference":[{"key":"9503_CR1","doi-asserted-by":"crossref","unstructured":"Abraham, C., Cornillon, P. A., Matzner-Lber, E., & Molinari, N. (2003). Unsupervised curve clustering using B-splines. Scandinavian Journal of Statistics, 30, 581\u2013595.","DOI":"10.1111\/1467-9469.00350"},{"key":"9503_CR2","doi-asserted-by":"crossref","unstructured":"Centofanti, F., Lepore, A., & Palumbo, B. (2022). Sparse and smooth functional data clustering. Statistical Papers, arXiv:2103.15224v2.","DOI":"10.32614\/CRAN.package.sasfunclust"},{"key":"9503_CR3","doi-asserted-by":"crossref","unstructured":"Chamroukhi, F., & Nguyen, H. D. (2019). Model-based clustering and classification of functional data. WIREs Data Mining & Knowledge Discovery, 2019(9), e1298.","DOI":"10.1002\/widm.1298"},{"key":"9503_CR4","doi-asserted-by":"crossref","unstructured":"Chiou, J. M., & Li, P. L. (2007). Functional clustering and identifying substructures of longitudinal data. Journal of the Royal Statistical Society. Series B, 69, 679\u2013699.","DOI":"10.1111\/j.1467-9868.2007.00605.x"},{"key":"9503_CR5","doi-asserted-by":"publisher","first-page":"1684","DOI":"10.1198\/016214508000000814","volume":"103","author":"JM Chiou","year":"2008","unstructured":"Chiou, J. M., & Li, P. L. (2008). Correlation-based functional clustering via subspace projection. Journal of the American Statistical Association, 103, 1684\u20131692.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12859-017-1996-y","volume":"19","author":"DS Chiu","year":"2018","unstructured":"Chiu, D. S., & Talhouk, A. (2018). diceR: An R package for class discovery using an ensemble driven approach. BMC Bioinformatics, 19, 1\u20134.","journal-title":"BMC Bioinformatics"},{"key":"9503_CR7","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1080\/01621459.1994.10476459","volume":"89","author":"RD Cook","year":"1994","unstructured":"Cook, R. D. (1994). On the interpretation of regression plots. Journal of the American Statistical Association, 89, 177\u2013189.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR8","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1214\/aos\/1021379861","volume":"30","author":"RD Cook","year":"2002","unstructured":"Cook, R. D., & Li, B. (2002). Dimension reduction for the conditional mean in regression. The Annals of Statistics, 30, 455\u2013474.","journal-title":"The Annals of Statistics"},{"key":"9503_CR9","volume-title":"Local polynomial modeling and its applications","author":"J Fan","year":"1996","unstructured":"Fan, J., & Gijbels, I. (1996). Local polynomial modeling and its applications. London: Chapman and Hall."},{"key":"9503_CR10","doi-asserted-by":"crossref","unstructured":"Ferraro, M. B., Giordani, P., & Serafini, A. (2019). Fclust: An R package for fuzzy clustering. The R Journal, 11, 1\u201318.","DOI":"10.32614\/RJ-2019-017"},{"key":"9503_CR11","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s00357-005-0013-8","volume":"22","author":"LA Garc\u00eda-Escudero","year":"2005","unstructured":"Garc\u00eda-Escudero, L. A., & Gordaliza, A. (2005). A proposal for robust curve clustering. Journal of Classification, 22, 185\u2013201.","journal-title":"Journal of Classification"},{"key":"9503_CR12","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1111\/j.1541-0420.2012.01828.x","volume":"69","author":"M Giacofci","year":"2013","unstructured":"Giacofci, M., Lambert-Lacroix, S., Marot, G., & Picard, F. (2013). Wavelet-based clustering for mixed-effects functional models in high dimension. Biometrics, 69, 31\u201340.","journal-title":"Biometrics"},{"key":"9503_CR13","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1198\/016214505000000187","volume":"101","author":"NA Heard","year":"2006","unstructured":"Heard, N. A., Holmes, C. C., & Stephens, D. A. (2006). A quantitative study of gene regulation involved in the immune response of anopheline mosquitoes: An application of Bayesian hierarchical clustering of curves. Journal of the American Statistical Association, 101, 18\u201329.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR14","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193\u2013218.","journal-title":"Journal of Classification"},{"key":"9503_CR15","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.csda.2012.12.004","volume":"71","author":"J Jacques","year":"2014","unstructured":"Jacques, J., & Preda, C. (2014). Model-based clustering for multivariate functional data. Computational Statistics & Data Analysis, 71, 92\u2013106.","journal-title":"Computational Statistics & Data Analysis"},{"key":"9503_CR16","volume-title":"Algorithms for clustering data","author":"AK Jain","year":"1988","unstructured":"Jain, A. K., & Dubes, R. C. (1988). Algorithms for clustering data. Englewood Cliffs: Prentice Hall."},{"key":"9503_CR17","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1198\/016214503000189","volume":"98","author":"GM James","year":"2003","unstructured":"James, G. M., & Sugar, C. A. (2003). Clustering for sparsely sampled functional data. Journal of the American Statistical Association, 98, 397\u2013408.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR18","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1002\/cjs.11680","volume":"50","author":"J Jiang","year":"2022","unstructured":"Jiang, J., Lin, H., Peng, H., Fan, G. Z., & Li, Y. (2022). Cluster analysis with regression of non-Gaussian functional data on covariates. Canadian Journal of Statistics, 50, 221\u2013240.","journal-title":"Canadian Journal of Statistics"},{"key":"9503_CR19","doi-asserted-by":"crossref","unstructured":"John, C. R., Watson, D., Barnes, M. R., Pitzalis, C., & Lewis, M. (2020). Spectrum: Fast density-aware spectral clustering for single and multi-omic data. Bioinformatics, 36, 1159\u20131166.","DOI":"10.1093\/bioinformatics\/btz704"},{"key":"9503_CR20","doi-asserted-by":"crossref","unstructured":"Li, K. C. (1991). Sliced inverse regression for dimension reduction (with discussion). Journal of the American Statistical Association, 86, 316\u2013342.","DOI":"10.2307\/2290563"},{"key":"9503_CR21","doi-asserted-by":"crossref","unstructured":"Li, K. C. (1992). On principal Hessian directions for data visualization and dimension reduction: Another application of Stein\u2019s lemma. Journal of the American Statistical Association, 87, 1025\u20131039.","DOI":"10.1080\/01621459.1992.10476258"},{"key":"9503_CR22","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1198\/016214503388619139","volume":"98","author":"KC Li","year":"2003","unstructured":"Li, K. C., Aragon, Y., Shedden, K., & Agnan, C. T. (2003). Dimension reduction for multivariate response data. Journal of the American Statistical Association, 98, 99\u2013109.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR23","doi-asserted-by":"crossref","unstructured":"Lue, H. H. (2009). Sliced inverse regression for multivariate response regression. Journal of Statistical Planning and Inference, 139, 2656\u20132664.","DOI":"10.1016\/j.jspi.2008.12.006"},{"key":"9503_CR24","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/s00180-010-0192-6","volume":"25","author":"HH Lue","year":"2010","unstructured":"Lue, H. H. (2010). On principal Hessian directions for multivariate response regressions. Computational Statistics, 25, 619\u2013632.","journal-title":"Computational Statistics"},{"key":"9503_CR25","doi-asserted-by":"publisher","first-page":"776","DOI":"10.1080\/00949655.2019.1572145","volume":"89","author":"HH Lue","year":"2019","unstructured":"Lue, H. H. (2019). Pairwise directions estimation for multivariate response regression data. Journal of Statistical Computation and Simulation, 89, 776\u2013794.","journal-title":"Journal of Statistical Computation and Simulation"},{"key":"9503_CR26","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1198\/016214508000000247","volume":"103","author":"P Ma","year":"2008","unstructured":"Ma, P., & Zhong, W. (2008). Penalized clustering of large-scale functional data with multiple covariates. Journal of the American Statistical Association, 103, 625\u2013636.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR27","doi-asserted-by":"publisher","unstructured":"Page, G. L., Quintana, F. A., & Dahl, D. B. (2022). Dependent modeling of temporal sequences of random partitions. Journal of Computational and Graphical Statistics, 1\u201314,. https:\/\/doi.org\/10.1080\/10618600.2021.1987255","DOI":"10.1080\/10618600.2021.1987255"},{"key":"9503_CR28","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1214\/08-AOAS172","volume":"2","author":"J Peng","year":"2008","unstructured":"Peng, J., & M\u00fcller, H.-G. (2008). Distance-based clustering of sparsely observed stochastic processes, with applications to online auctions. The Annals of Applied Statistics, 2, 1056\u20131077.","journal-title":"The Annals of Applied Statistics"},{"key":"9503_CR29","doi-asserted-by":"crossref","unstructured":"Quintana, F. A., & Iglesias, P. L. (2003). Bayesian clustering and product partition models. Journal of the Royal Statistical Society. Series B, 65, 557\u2013574.","DOI":"10.1111\/1467-9868.00402"},{"key":"9503_CR30","doi-asserted-by":"publisher","first-page":"846","DOI":"10.1080\/01621459.1971.10482356","volume":"66","author":"WM Rand","year":"1971","unstructured":"Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66, 846\u2013850.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR31","doi-asserted-by":"publisher","first-page":"1169","DOI":"10.1007\/s11222-017-9786-y","volume":"28","author":"R Rastelli","year":"2018","unstructured":"Rastelli, R., & Friel, N. (2018). Optimal Bayesian estimators for latent variable cluster models. Statistics and Computing, 28, 1169\u20131186.","journal-title":"Statistics and Computing"},{"key":"9503_CR32","doi-asserted-by":"crossref","unstructured":"Ray, S., & Mallick, B. (2006). Functional clustering by Bayesian wavelet methods. Journal of the Royal Statistical Society. Series B, 305-332.","DOI":"10.1111\/j.1467-9868.2006.00545.x"},{"key":"9503_CR33","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1198\/016214504000001574","volume":"100","author":"N Serban","year":"2005","unstructured":"Serban, N., & Wasserman, L. (2005). CATS: Clustering after transformation and smoothing. Journal of the American Statistical Association, 100, 990\u2013999.","journal-title":"Journal of the American Statistical Association"},{"key":"9503_CR34","first-page":"363","volume":"64","author":"Y Xia","year":"2002","unstructured":"Xia, Y., Tong, H., Li, W. K., & Zhu, L. X. (2002). An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society. Series B, 64, 363\u2013410.","journal-title":"Series B"},{"key":"9503_CR35","first-page":"793","volume":"61","author":"L Yang","year":"1999","unstructured":"Yang, L., & Tschernig, R. (1999). Multivariate bandwidth selection for local linear regression. Journal of the Royal Statistical Society. Series B, 61, 793\u2013815.","journal-title":"Series B"},{"key":"9503_CR36","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1093\/bioinformatics\/17.9.763","volume":"17","author":"KY Yeung","year":"2001","unstructured":"Yeung, K. Y., & Ruzzo, W. L. (2001). Principal component analysis for clustering gene expression data. Bioinformatics, 17, 763\u2013774.","journal-title":"Bioinformatics"}],"container-title":["Journal of Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-025-09503-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00357-025-09503-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-025-09503-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T01:45:23Z","timestamp":1763171123000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00357-025-09503-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,17]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["9503"],"URL":"https:\/\/doi.org\/10.1007\/s00357-025-09503-8","relation":{},"ISSN":["0176-4268","1432-1343"],"issn-type":[{"type":"print","value":"0176-4268"},{"type":"electronic","value":"1432-1343"}],"subject":[],"published":{"date-parts":[[2025,3,17]]},"assertion":[{"value":"28 February 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 March 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This research does not contain any studies with human participations or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"The author declares no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}