An Efficient Smoothing Proximal Gradient Algorithm for Convex Clustering

TL;DR

This paper introduces Sproga, a smoothing proximal gradient algorithm that significantly improves the efficiency and scalability of convex clustering, outperforming existing methods and traditional clustering algorithms.

Contribution

Develops a novel Sproga algorithm that is faster and more memory-efficient than existing convex clustering methods, enabling broader application.

Findings

Sproga is 10-100 times faster than ADMM and AMA algorithms.

Sproga requires at least 10 times less memory than existing convex clustering methods.

Sproga outperforms K-means and hierarchical clustering in accuracy and efficiency.

Abstract

Cluster analysis organizes data into sensible groupings and is one of fundamental modes of understanding and learning. The widely used K-means and hierarchical clustering methods can be dramatically suboptimal due to local minima. Recently introduced convex clustering approach formulates clustering as a convex optimization problem and ensures a globally optimal solution. However, the state-of-the-art convex clustering algorithms, based on the alternating direction method of multipliers (ADMM) or the alternating minimization algorithm (AMA), require large computation and memory space, which limits their applications. In this paper, we develop a very efficient smoothing proximal gradient algorithm (Sproga) for convex clustering. Our Sproga is faster than ADMM- or AMA-based convex clustering algorithms by one to two orders of magnitude. The memory space required by Sproga is less than that required by ADMM and AMA by at least one order of magnitude. Computer simulations and real data analysis show that Sproga outperforms several well known clustering algorithms including K-means and hierarchical clustering. The efficiency and superior performance of our algorithm will help convex clustering to find its wide application.