Transductive Kernels for Gaussian Processes on Graphs

TL;DR

This paper introduces a new transductive kernel for graph-based semi-supervised learning that leverages graph and feature data as Hilbert spaces, improving learning efficiency on limited data and complex non-Euclidean structures.

Contribution

The paper presents a generalized, transductive kernel for graphs with node features, unifying various kernel models and enhancing semi-supervised learning on graphs.

Findings

Improved learning with fewer training points.

Effective handling of highly non-Euclidean data.

Successful semi-supervised classification on diverse graphs.

Abstract

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantages using synthetic data where the distribution of the whole graph can inform the pattern of the labels. Finally, by utilizing a flexible polynomial of the graph Laplacian within the kernel, the model also performed effectively in semi-supervised classification on graphs of various levels of homophily.