Sparse Convex Clustering

TL;DR

This paper introduces Sparse Convex Clustering, a method that enhances high-dimensional clustering by simultaneously performing clustering and feature selection using a regularized convex framework.

Contribution

It proposes a novel regularization-based convex clustering method with adaptive group-lasso penalty for feature selection in high-dimensional data.

Findings

Improved clustering performance with feature selection in high-dimensional settings

Development of a stability-based tuning criterion

Theoretical estimator for degrees of freedom

Abstract

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 paper, 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. In order to optimally balance the tradeoff between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. In theory, we provide an unbiased estimator for the degrees of freedom of the proposed sparse convex clustering method. Finally, the effectiveness of the sparse convex clustering is examined through a variety of numerical experiments and a real data application.