Graph diffusion kernel LMS using random Fourier features

This work introduces kernel adaptive graph filters that operate in the reproducing kernel Hilbert space. We propose a centralized graph kernel least mean squares (GKLMS) approach for identifying the nonlinear graph filters. The principles of coherence-check and random Fourier features (RFF) are used to reduce the dictionary size. Additionally, we leverage the graph structure to derive the graph diffusion KLMS (GDKLMS). The proposed GDKLMS requires only single-hop communication during successive time instants, making it viable for real-time network-based applications. In the distributed implementation, usage of RFF avoids the requirement of a centralized pre-trained dictionary in the case of coherence-check. Finally, the performance of the proposed algorithms is demonstrated in modeling a nonlinear graph filter via numerical examples. The results show that centralized and distributed implementations effectively model the nonlinear graph filters, whereas the random-feature-based solutions are shown to outperform coherence-check based solutions