Distributed Clustering and Learning Over Networks

TL;DR

This paper introduces an adaptive clustering and learning algorithm for distributed networks, enabling agents to identify their clusters and cooperate effectively, improving learning accuracy while minimizing false cooperation.

Contribution

It presents a novel adaptive scheme for clustering in distributed networks, with detailed analysis of error probabilities and convergence properties.

Findings

Error probabilities decay exponentially with step-sizes.

Agents can reliably identify their clusters with high probability.

The algorithm improves estimation accuracy over networks.

Abstract

Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this work, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and mis-detection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.