Statistical Properties of Convex Clustering

In this manuscript, we study the statistical properties of convex clustering. Through its dual problem, we establish that convex clustering is closely related to single linkage clustering. In addition, we derive the range of tuning parameter for convex clustering that yields a non-trivial solution. We also provide an unbiased estimate of the degrees of freedom, and provide a finite sample bound for the prediction error for convex clustering. We compare convex clustering to some traditional clustering methods in a simulation study.