Statistical Properties of Convex Clustering

TL;DR

This paper investigates the statistical characteristics of convex clustering, linking it to other clustering methods, and provides theoretical insights and bounds to improve understanding and application.

Contribution

It establishes the relationship between convex clustering and other methods, derives tuning parameter ranges, and offers theoretical bounds and estimates for convex clustering.

Findings

Convex clustering is closely related to single linkage and k-means clustering.

Provides a finite sample bound for prediction error.

Offers an unbiased estimate of degrees of freedom.

Abstract

In this manuscript, we study the statistical properties of convex clustering. We establish that convex clustering is closely related to single linkage hierarchical clustering and $k$-means 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 simulation studies.