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Tao Jiang(tao.jianguwaterloo.ca) Abstract: Sumofnorms clustering is a method for assigning $n$ points in $\R^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sumofnorms clustering is guaranteed to recover a mixture of Gaussians under the restriction that the number of samples is not too large. The purpose of this note is to lift this restriction, i.e., show that sumofnorms clustering with equal weights can recover a mixture of Gaussians even as the number of samples tends to infinity. Our proof relies on an interesting characterization of clusters computed by sumofnorms clustering that was developed inside a proof of the agglomeration conjecture by Chiquet et al. Because we believe this theorem has independent interest, we restate and reprove the Chiquet et al.\ result herein. Keywords: sumofnorms clustering; convex clustering; recovery guarantee; mixture of Gaussians Category 1: Applications  Science and Engineering (Statistics ) Category 2: Linear, Cone and Semidefinite Programming (SecondOrder Cone Programming ) Citation: Download: [PDF] Entry Submitted: 02/19/2019 Modify/Update this entry  
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