{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T22:42:20Z","timestamp":1740177740426,"version":"3.37.3"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03n04","funder":[{"name":"National Science Foundation","award":["DMS 1818821"],"award-info":[{"award-number":["DMS 1818821"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv. Data Sci. Adapt. Data Anal."],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p> A new method for hierarchical clustering of data points is presented. It combines treelets, a particular multiresolution decomposition of data, with a mapping on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT), uses this mapping to go from a hierarchical clustering over attributes (the natural output of treelets) to a hierarchical clustering over data. KT effectively substitutes the correlation coefficient matrix used in treelets with a symmetric and positive semi-definite matrix efficiently constructed from a symmetric and positive semi-definite kernel function. Unlike most clustering methods, which require data sets to be numeric, KT can be applied to more general data and yields a multiresolution sequence of orthonormal bases on the data directly in feature space. The effectiveness and potential of KT in clustering analysis are illustrated with some examples. <\/jats:p>","DOI":"10.1142\/s2424922x19500062","type":"journal-article","created":{"date-parts":[[2019,6,28]],"date-time":"2019-06-28T08:08:17Z","timestamp":1561709297000},"page":"1950006","source":"Crossref","is-referenced-by-count":0,"title":["Kernel Treelets"],"prefix":"10.1142","volume":"11","author":[{"given":"Hedi","family":"Xia","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0867-0151","authenticated-orcid":false,"given":"Hector D.","family":"Ceniceros","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, USA"}]}],"member":"219","published-online":{"date-parts":[[2019,10,14]]},"reference":[{"key":"S2424922X19500062BIB001","first-page":"821","volume":"25","author":"Aizerman M. 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