Convex Clustering through MM: An Efficient Algorithm to Perform Hierarchical Clustering

TL;DR

This paper introduces CCMM, an efficient majorization-minimization algorithm for convex clustering that scales to large datasets and guarantees a complete hierarchical structure, significantly improving computational efficiency and robustness.

Contribution

The paper presents CCMM, a novel iterative algorithm for convex clustering that enhances scalability and ensures hierarchical completeness, addressing limitations of previous methods.

Findings

Successfully clusters over one million objects in 7D space within 51 seconds.

Ensures the hierarchical clustering structure terminates in a single cluster.

Achieves high efficiency and scalability compared to existing convex clustering algorithms.

Abstract

Convex clustering is a modern method with both hierarchical and $k$-means clustering characteristics. Although convex clustering can capture complex clustering structures hidden in data, the existing convex clustering algorithms are not scalable to large data sets with sample sizes greater than several thousands. Moreover, it is known that convex clustering sometimes fails to produce a complete hierarchical clustering structure. This issue arises if clusters split up or the minimum number of possible clusters is larger than the desired number of clusters. In this paper, we propose convex clustering through majorization-minimization (CCMM) -- an iterative algorithm that uses cluster fusions and a highly efficient updating scheme derived using diagonal majorization. Additionally, we explore different strategies to ensure that the hierarchical clustering structure terminates in a single cluster. With a current desktop computer, CCMM efficiently solves convex clustering problems featuring over one million objects in seven-dimensional space, achieving a solution time of 51 seconds on average.