  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.
