A Euclidean Distance Matrix Model for Convex Clustering

TL;DR

This paper introduces a Euclidean distance matrix model for convex clustering based on the sum-of-norms framework, along with an efficient algorithm, demonstrating superior performance through extensive experiments.

Contribution

It proposes a novel Euclidean distance matrix model for convex clustering and develops an efficient majorization penalty algorithm for its solution.

Findings

The model achieves accurate clustering results.

The algorithm demonstrates high efficiency and scalability.

Numerical experiments confirm the model's effectiveness.

Abstract

Clustering has been one of the most basic and essential problems in unsupervised learning due to various applications in many critical fields. The recently proposed sum-of-norms (SON) model by Pelckmans et al. (2005), Lindsten et al. (2011) and Hocking et al. (2011) has received a lot of attention. The advantage of the SON model is the theoretical guarantee in terms of perfect recovery, established by Sun et al. (2018). It also provides great opportunities for designing efficient algorithms for solving the SON model. The semismooth Newton based augmented Lagrangian method by Sun et al. (2018) has demonstrated its superior performance over the alternating direction method of multipliers (ADMM) and the alternating minimization algorithm (AMA). In this paper, we propose a Euclidean distance matrix model based on the SON model. An efficient majorization penalty algorithm is proposed to solve the resulting model. Extensive numerical experiments are conducted to demonstrate the efficiency of the proposed model and the majorization penalty algorithm.