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This recently proposed approach has been gaining in popularity; however, its asymptotic properties have remained mostly unknown. Our analysis is based on a novel representation of the sample clustering procedure as a sequence of cluster splits determined by a sequence of maximization problems. We use this representation to provide a simple and intuitive formulation for the population clustering procedure. We then demonstrate that the sample procedure consistently estimates its population analogue and we derive the corresponding rates of convergence. The proof conducts a careful simultaneous analysis of a collection of M-estimation problems, whose cardinality grows together with the sample size. On the basis of the new perspectives gained from the asymptotic investigation, we propose a key post-processing modification of the original clustering framework. We show, both theoretically and empirically, that the resulting approach can be successfully used to estimate the number of clusters in the population. Using simulated data, we compare the proposed method with existing number-of-clusters and modality assessment approaches and obtain encouraging results. We also demonstrate the applicability of our clustering method to the detection of cellular subpopulations in a single-cell virology study.<\/jats:p>","DOI":"10.1111\/rssb.12226","type":"journal-article","created":{"date-parts":[[2017,2,13]],"date-time":"2017-02-13T06:33:07Z","timestamp":1486967587000},"page":"1527-1546","source":"Crossref","is-referenced-by-count":29,"title":["Convex Clustering via<i>l<\/i>\u00a01 Fusion Penalization"],"prefix":"10.1093","volume":"79","author":[{"given":"Peter","family":"Radchenko","sequence":"first","affiliation":[{"name":"University of Southern California , Los Angeles , USA"},{"name":"University of Sydney Business School , Darlington , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gourab","family":"Mukherjee","sequence":"additional","affiliation":[{"name":"University of Southern California , Los Angeles , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,2,13]]},"reference":[{"key":"2023022101102820000_rssb12226-cit-0001","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1111\/j.2517-6161.1985.tb01331.x","article-title":"Estimation and hypothesis testing in finite mixture models","volume":"47","author":"Aitkin","year":"1985","journal-title":"J. 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