Exploring Graph Classification Techniques Under Low Data Constraints: A Comprehensive Study

This survey paper presents a brief overview of recent research on graph data augmentation and few-shot learning. It covers various techniques for graph data augmentation, including node and edge perturbation, graph coarsening, and graph generation, as well as the latest developments in few-shot learning, such as meta-learning and model-agnostic meta-learning. The paper explores these areas in depth and delves into further sub classifications. Rule based approaches and learning based approaches are surveyed under graph augmentation techniques. Few-Shot Learning on graphs is also studied in terms of metric learning techniques and optimization-based techniques. In all, this paper provides an extensive array of techniques that can be employed in solving graph processing problems faced in low-data scenarios

QDC: Quantum Diffusion Convolution Kernels on Graphs

Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods

Generalized heat kernel signatures

In this work we propose a generalization of the Heat Kernel Signature (HKS). The HKS is a point signature derived from the heat kernel of the Laplace-Beltrami operator of a surface. In the theory of exterior calculus on a Riemannian manifold, the Laplace-Beltrami operator of a surface is a special case of the Hodge Laplacian which acts on r-forms, i. e. the Hodge Laplacian on 0-forms (functions) is the Laplace-Beltrami operator. We investigate the usefulness of the heat kernel of the Hodge Laplacian on 1-forms (which can be seen as the vector Laplacian) to derive new point signatures which are invariant under isometric mappings. A similar approach used to obtain the HKS yields a symmetric tensor field of second order; for easier comparability we consider several scalar tensor invariants. Computed examples show that these new point signatures are especially interesting for surfaces with boundary