Scalable Algorithms for Convex Clustering

Convex clustering is an appealing approach to many classical clustering problems. It stands out among standard methods as it enjoys the existence of a unique global optimal solution. Despite this advantage, convex clustering has not been widely adopted, due to its computationally intensive nature. To address this obstacle, especially in the “big data” setting, we introduce a Scalable cOnvex cLustering AlgoRithm via Parallel Coordinate Descent Method (SOLAR-PCDM) that improves the algorithm’s scalability by combining a parallelizable algorithm with a compression strategy. This idea is in line with the rise and ever increasing availability of high performance computing systems built around multi-core processors, GPU-accelerators, and computer clusters. SOLARPCDM consists of two parts. In the first part, we develop a method called weighted convex clustering to recover the solution path by formulating a sequence of smaller equivalent optimization problems. In the second part, we utilize the Parallel Coordinate Descent Method (PCDM) to solve a specific convex clustering problem. We demonstrate the correctness and scalability of our algorithm on both simulated and real data examples.