Distributed Gradient Clustering: Convergence and the Effect of Initialization

TL;DR

This paper investigates how initialization affects distributed gradient clustering algorithms and introduces a new initialization method inspired by K-means++ that enhances performance.

Contribution

It analyzes the impact of center initialization on distributed clustering and proposes a novel distributed initialization scheme improving robustness and accuracy.

Findings

Distributed methods are more resilient to initialization effects than centralized ones.

The proposed initialization scheme improves clustering performance over random initialization.

Numerical experiments demonstrate the effectiveness of the new initialization method.

Abstract

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.