Federated K-Means Clustering via Dual Decomposition-based Distributed Optimization

TL;DR

This paper introduces a dual decomposition-based distributed optimization method for federated K-means clustering, aiming to improve privacy preservation and computational efficiency in large-scale machine learning.

Contribution

It presents a novel application of dual decomposition to distributed K-means clustering, including a mixed-integer programming formulation and evaluation of optimization algorithms.

Findings

The approach enables distributed training of K-means with consensus constraints.

Evaluation shows potential of dual methods despite weak integer relaxations.

Future work may improve efficiency for large-scale federated clustering.

Abstract

The use of distributed optimization in machine learning can be motivated either by the resulting preservation of privacy or the increase in computational efficiency. On the one hand, training data might be stored across multiple devices. Training a global model within a network where each node only has access to its confidential data requires the use of distributed algorithms. Even if the data is not confidential, sharing it might be prohibitive due to bandwidth limitations. On the other hand, the ever-increasing amount of available data leads to large-scale machine learning problems. By splitting the training process across multiple nodes its efficiency can be significantly increased. This paper aims to demonstrate how dual decomposition can be applied for distributed training of $ K $-means clustering problems. After an overview of distributed and federated machine learning, the mixed-integer quadratically constrained programming-based formulation of the $ K $-means clustering training problem is presented. The training can be performed in a distributed manner by splitting the data across different nodes and linking these nodes through consensus constraints. Finally, the performance of the subgradient method, the bundle trust method, and the quasi-Newton dual ascent algorithm are evaluated on a set of benchmark problems. While the mixed-integer programming-based formulation of the clustering problems suffers from weak integer relaxations, the presented approach can potentially be used to enable an efficient solution in the future, both in a central and distributed setting.