Multi-kernel Regression For Graph Signal Processing

TL;DR

This paper introduces a multi-kernel regression approach for graph signal processing, leveraging convex optimization and regularization to improve signal smoothness estimation over graphs.

Contribution

It proposes a novel multi-kernel regression method with an efficient convex optimization solution for graph signal smoothness estimation.

Findings

Outperforms standard kernel methods in simulations

Efficient convex optimization approach developed

Effective for real-world graph signals

Abstract

We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and pro- pose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency of the multi-kernel based approach over a standard kernel based approach.