  Convex clustering is a recent stable alternative to hierarchical clustering.
It formulates the recovery of progressively coalescing clusters as a
regularized convex problem. While convex clustering was originally designed for
handling Euclidean distances between data points, in a growing number of
applications, the data is directly characterized by a similarity matrix or
weighted graph. In this paper, we extend the robust hierarchical clustering
approach to these broader classes of similarities. Having defined an
appropriate convex objective, the crux of this adaptation lies in our ability
to provide: (a) an efficient recovery of the regularization path and (b) an
empirical demonstration of the use of our method. We address the first
challenge through a proximal dual algorithm, for which we characterize both the
theoretical efficiency as well as the empirical performance on a set of
experiments. Finally, we highlight the potential of our method by showing its
application to several real-life datasets, thus providing a natural extension
to the current scope of applications of convex clustering.
