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.

本文介绍了一种新的聚类方法——Sparse Convex Clustering，该方法采用一种正则化形式的凸聚类方法来进行特征选择，并使用基于聚类稳定性的调整标准来优化聚类效果。作者通过多种数值实验和真实数据应用验证了该聚类方法的有效性。

稀疏凸聚类