Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphs

TL;DR

This paper introduces a method to optimally configure the Gaussian kernel variance in the single-kernel Gradraker algorithm for predicting node values in networks, enhancing its adaptability and performance.

Contribution

It proposes two analysis variables to determine the Gaussian kernel variance for SKG, improving understanding and configuration of the model.

Findings

Variables effectively guide kernel variance selection

Simulations demonstrate improved prediction accuracy

Method adapts to different network structures

Abstract

This paper discusses a special kind of a simple yet possibly powerful algorithm, called single-kernel Gradraker (SKG), which is an adaptive learning method predicting unknown nodal values in a network using known nodal values and the network structure. We aim to find out how to configure the special kind of the model in applying the algorithm. To be more specific, we focus on SKG with a Gaussian kernel and specify how to find a suitable variance for the kernel. To do so, we introduce two variables with which we are able to set up requirements on the variance of the Gaussian kernel to achieve (near-) optimal performance and can better understand how SKG works. Our contribution is that we introduce two variables as analysis tools, illustrate how predictions will be affected under different Gaussian kernels, and provide an algorithm finding a suitable Gaussian kernel for SKG with knowledge about the training network. Simulation results on real datasets are provided.