Decentralized clustering for node-variant graph filtering with graph diffusion LMS

In this work, we consider the problem of estimating the coefficients of linear shift-invariant FIR graph filters. We assume hybrid node-varying graph filters where the network is decomposed into clusters of nodes and, within each cluster, all nodes have the same filter coefficients to estimate. We assume that there is no prior information on the clusters composition and that the nodes do not know which other nodes share the same estimation task. We are interested in distributed, adaptive, and collaborative solutions. In order to limit the cooperation between clustered agents sharing the same estimation task, we propose an extended diffusion preconditioned LMS strategy allowing the nodes to perform automatic network clustering. Simulation results illustrate the effectiveness of the proposed unsupervised method for clustering nodes into clusters and collaborative estimation.