Gaussian Kernel Variance For an Adaptive Learning Method on Signals Over Graphs
This work addresses a specific configuration challenge for adaptive learning on graph signals, representing an incremental improvement in optimizing kernel parameters for network-based prediction tasks.
The paper tackles the problem of configuring the Gaussian kernel variance for the single-kernel Gradraker (SKG) adaptive learning method to predict unknown nodal values in networks, resulting in a method to achieve near-optimal performance by introducing two analysis variables and providing an algorithm for kernel selection.
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.