Reduction Techniques for Graph-Based Convex Clustering

The Graph-based Convex Clustering (GCC) method has gained increasing attention recently. The GCC method adopts a fused regularizer to learn the cluster centers and obtains a geometric clusterpath by varying the regularization parameter. One major limitation is that solving the GCC model is computationally expensive. In this paper, we develop efficient graph reduction techniques for the GCC model to eliminate edges, each of which corresponds to two data points from the same cluster, without solving the optimization problem in the GCC method, leading to improved computational efficiency. Specifically, two reduction techniques are proposed according to tree-based and cyclic-graph-based convex clustering methods separately. The proposed reduction techniques are appealing since they only need to scan the data once with negligibly additional cost and they are independent of solvers for the GCC method, making them capable of improving the efficiency of any existing solver. Experiments on both synthetic and real-world datasets show that our methods can largely improve the efficiency of the GCC model.