A Matrix Model for Adaptive Graph Filtering Using a Generalized Mean-sets Theory’s Approach

Integrating Mean-sets theory employing generalized graph or group-theoretic tools and techniques into adaptive graph filtering can lead to more effective resilient filtering processes, particularly in challenging environments with clutter or uncertainty. In this paper, we show that under some crucial smoothing assumptions, the generalized Mean-sets theory developped for negatively curved convex combination Polish metric spaces following the formal Means-sets probability theory’s approach from Natalia Mosina, provides a new useful system for some secure adaptive graph filtering processes. We use convex combination operations (in the sense of Terán and Molchanov) on both individual input graph signals and filters. Individual adaptive graph filters being independently adapted by space (dataset)-valued random variables, while the convexification operator on the underlying dataset acts as a flexible theoretical instrument for preserving some good features of the standard scheme, like privacy of their informative trends, and looks more robust to changes. We exhibit a graph matrix model from a system of convex combination of two adaptive finite impulse response (FIR) graph filters processing a sampled-weighted mean-set (expectation) of some transversal graph signals with finite length <i>N</i> ≥ 2.