{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:16:14Z","timestamp":1769753774763,"version":"3.49.0"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:00:00Z","timestamp":1649721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses spheres, an approach we refer to as spherelets. We develop spherical principal components analysis (SPCA), and provide theory on the convergence rate for global and local SPCA, while showing that spherelets can provide lower covering numbers and mean squared errors for many manifolds. Results relative to state-of-the-art competitors show gains in ability to accurately approximate manifolds with fewer components. Unlike most competitors, which simply output lower-dimensional features, our approach projects data onto the estimated manifold to produce fitted values that can be used for model assessment and cross validation. The methods are illustrated with applications to multiple data sets.<\/jats:p>","DOI":"10.1111\/rssb.12508","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T16:41:48Z","timestamp":1649781708000},"page":"1129-1149","source":"Crossref","is-referenced-by-count":11,"title":["Efficient Manifold Approximation with Spherelets"],"prefix":"10.1093","volume":"84","author":[{"given":"Didong","family":"Li","sequence":"first","affiliation":[{"name":"Department of Computer Science , Princeton , New Jersey , USA , Los Angeles , California , USA"},{"name":"Princeton University , Princeton , New Jersey , USA , Los Angeles , California , USA"},{"name":"Department of Biostatistics , Princeton , New Jersey , USA , Los Angeles , California , USA"},{"name":"University of California , Princeton , New Jersey , USA , Los Angeles , California , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minerva","family":"Mukhopadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , Kanpur , Uttar Pradesh , India"},{"name":"Indian Institute of Technology , Kanpur , Uttar Pradesh , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David B.","family":"Dunson","sequence":"additional","affiliation":[{"name":"Department of Statistical Science , Durham , North Carolina , USA"},{"name":"Duke University , Durham , North Carolina , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,4,12]]},"reference":[{"key":"2023030906302116800_","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1214\/18-AOS1685","article-title":"Nonasymptotic rates for manifold, tangent space and curvature estimation","volume":"47","author":"Aamari","year":"2019","journal-title":"The Annals of 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