Sparse Convex Clustering

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.

References in corpus (4)

• Natural Scales in Geographical Patterns
• Proceedings of the 29th International Conference on Machine Learning (ICML-12)
• Splitting Methods for Convex Clustering
• The degrees of freedom of the Group Lasso for a General Design

Cited by in corpus (15)

• Dynamic Visualization and Fast Computation for Convex Clustering via Algorithmic Regularization
• Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data
• Fast and Interpretable Consensus Clustering via Minipatch Learning
• Sparse principal component regression via singular value decomposition approach
• A Semi-Definite Programming approach to low dimensional embedding for unsupervised clustering
• An Efficient Smoothing Proximal Gradient Algorithm for Convex Clustering
• A Centroid Auto-Fused Hierarchical Fuzzy c-Means Clustering
• Simultaneous Grouping and Denoising via Sparse Convex Wavelet Clustering
• Resistant convex clustering: How does the fusion penalty enhance resistantance?
• On Convex Clustering Solutions
• Selective inference after convex clustering with ${\ell }_1$ penalization
• A New Algorithm for Convex Biclustering and Its Extension to the Compositional Data
• Supervised Convex Clustering
• Sparse Group Fused Lasso for Model Segmentation
• Bayesian sparse convex clustering via global-local shrinkage priors