## A framework for feature selection in clustering.(English)Zbl 1392.62194

Summary: We consider the problem of clustering observations using a potentially large set of features. One might expect that the true underlying clusters present in the data differ only with respect to a small fraction of the features, and will be missed if one clusters the observations using the full set of features. We propose a novel framework for sparse clustering, in which one clusters the observations using an adaptively chosen subset of the features. The method uses a lasso-type penalty to select the features. We use this framework to develop simple methods for sparse $$K$$-means and sparse hierarchical clustering. A single criterion governs both the selection of the features and the resulting clusters. These approaches are demonstrated on simulated and genomic data.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62J07 Ridge regression; shrinkage estimators (Lasso) 62P10 Applications of statistics to biology and medical sciences; meta analysis

sparcl
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