Kernel Based Reconstruction for Generalized Graph Signal Processing

TL;DR

This paper introduces a kernel ridge regression approach for signal reconstruction in generalized graph signal processing, enabling distributed computation, online implementation, and Bayesian analysis, validated on real-world data.

Contribution

It proposes a novel kernel-based reconstruction method for GGSP, linking deterministic and Bayesian perspectives, with an online implementation and theoretical performance analysis.

Findings

Distributed solution for GGSP signal reconstruction.

Effective online implementation via random Fourier features.

Validated performance on real-world datasets.

Abstract

In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising an appropriate kernel, we show that this problem has a solution that can be evaluated in a distributed way. We interpret the problem and solution using both deterministic and Bayesian perspectives and link them to existing graph signal processing and GGSP frameworks. We then provide an online implementation via random Fourier features. Under the Bayesian framework, we investigate the statistical performance under the asymptotic sampling scheme. Finally, we validate our theory and methods on real-world datasets.