Greedy centroid initialization for federated K-means

Abstract

In this paper, our focus is on K-means within a federated setting, where clients retain their raw data on local devices, and the raw data never leaves the corresponding devices. Given the importance of initialization on the federated K-means algorithm, our objective is to find better initial centroids by utilizing the local data stored on each client. To this end, we start the centroid initialization at the clients, rather than at the server, since the server initially lacks any preliminary insight into the clients' data. The clients first select their local initial clusters, and subsequently share their clustering information (including cluster centroids and sizes) with the server. The server then employs a greedy algorithm to determine the global initial centroids based on the information received from the clients. Numerical results obtained from both synthetic and public datasets demonstrate that our proposed method can achieve better and more stable performance than three distinct federated K-means variants, and comparable performance to the centralized K-means algorithm.