Sparse Convex Clustering

Binhuan Wang, Yilong Zhang, Will Wei Sun, Yixin Fang

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex clustering has not yet been investigated in the high-dimensional clustering scenario, where the data contains a large number of features and many of them carry no information about the clustering structure. In this article, we demonstrate that the performance of convex clustering could be distorted when the uninformative features are included in the clustering. To overcome it, we introduce a new clustering method, referred to as Sparse Convex Clustering, to simultaneously cluster observations and conduct feature selection. The key idea is to formulate convex clustering in a form of regularization, with an adaptive group-lasso penalty term on cluster centers. To optimally balance the trade-off between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. Theoretically, we obtain a finite sample error bound for our estimator and further establish its variable selection consistency. The effectiveness of the proposed method is examined through a variety of numerical experiments and a real data application. Supplementary material for this article is available online.

Original languageEnglish (US)
Pages (from-to)393-403
Number of pages11
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Apr 3 2018


  • Convex clustering
  • Finite sample error
  • Group LASSO
  • High-dimensionality
  • Sparsity

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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