Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size
This work addresses the challenge of semi-supervised learning on graphs when only a small number of labeled training examples are available, which is an incremental improvement over existing methods.
The paper tackles the problem of semi-supervised graph learning with limited labeled data by introducing algorithms based on fractional heat kernel dynamics, which enhance Graph Neural Networks like GCNs and Graph Attention through adaptive multi-hop diffusion. The approach shows effectiveness on standard datasets, with computational feasibility achieved via Chebyshev polynomial approximations for large graphs.
In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the physics of parabolic evolution equations. We integrate the fractional heat kernel into Graph Neural Network architectures such as Graph Convolutional Networks and Graph Attention, enhancing their expressiveness through adaptive, multi-hop diffusion. By applying Chebyshev polynomial approximations, large graphs become computationally feasible. Motivating variational formulations demonstrate that by extending the classical diffusion model to fractional powers of the Laplacian, nonlocal interactions deliver more globally diffusing labels. The particular balance between supervision of known labels and diffusion across the graph is particularly advantageous in the case where only a small number of labeled training examples are present. We demonstrate the effectiveness of this approach on standard datasets.