Convergence Analysis of the Graph-Topology-Inference Kernel LMS Algorithm

Identifying directed connectivity patterns from nodal measurements is an important problem in network analysis. Recent works proposed to leverage the performance and flexibility of strategies operating in reproducing kernel Hilbert spaces (RKHS) to model nonlinear interactions between network agents. Moreover, several applications require online and efficient solutions, which motivated the consideration of distributed adaptive learning strategies inspired by algorithms such as the kernel least mean square (KLMS). Despite showing good performance, a thorough theoretical understanding of the behavior of such algorithms is still missing. This makes applying them in practice challenging, especially because the set-up of adaptive algorithms involves additional parameters like the step size and a dictionary of kernel functions. In this paper, we present a convergence analysis of the graph-topology-inference KLMS algorithm. Monte Carlo simulations demonstrate the accuracy of the theoretical models.