Clusterpath: An Algorithm for Clustering using Convex Fusion Penalties. We present a new clustering algorithm by proposing a convex relaxation of hierarchical clustering, which results in a family of objective functions with a natural geometric interpretation. We give efficient algorithms for calculating the continuous regularization path of solutions, and discuss relative advantages of the parameters. Our method experimentally gives state-of-the-art results similar to spectral clustering for non-convex clusters, and has the added benefit of learning a tree structure from the data.