Distributed Gradient Clustering: Convergence and the Effect of Initialization
This work addresses the problem of robust clustering in distributed settings for users with local data, though it is incremental as it builds on existing methods.
The paper investigates how center initialization affects the performance of distributed gradient-based clustering algorithms over networks, finding that these methods are more resilient to initialization than centralized approaches and that a novel distributed initialization scheme improves performance compared to random initialization.
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.