Understanding and Enhancing Graph Neural Networks From the Perspective of Partial Differential Equations

We understand graph neural networks from the perspective of partial diff erential equations. Firstly, based on the relationship between the partial diff erential equation and the propagation equation of graph neural networks, the topology and node features are treated as independent variables of the wave function to better combine the topological structure information of the graph with the node feature information. Secondly, the theoretical framework of the graph neural network model PGNN is established by the variable separation operation of the partial diff erential equation, which makes some existing models have diff erent degrees of PGNN approximation. Finally, experiments show that the model in this paper achieves good results on commonly used citation datasets

Revisiting Heterophily in Graph Convolution Networks by Learning Representations Across Topological and Feature Spaces

Graph convolution networks (GCNs) have been enormously successful in learning representations over several graph-based machine learning tasks. Specific to learning rich node representations, most of the methods have solely relied on the homophily assumption and have shown limited performance on the heterophilous graphs. While several methods have been developed with new architectures to address heterophily, we argue that by learning graph representations across two spaces i.e., topology and feature space GCNs can address heterophily. In this work, we experimentally demonstrate the performance of the proposed GCN framework over semi-supervised node classification task on both homophilous and heterophilous graph benchmarks by learning and combining representations across the topological and the feature spaces.Comment: Under Review Project Page: https://sites.google.com/iitgn.ac.in/hetgcn/hom

Neighborhood Homophily-based Graph Convolutional Network

Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies deepen networks or concatenate intermediate representations, which does not inherently change neighbor aggregation and introduces noise. Recent studies propose new metrics to characterize the homophily, but rarely consider the correlation of the proposed metrics and models. In this paper, we first design a new metric, Neighborhood Homophily (\textit{NH}), to measure the label complexity or purity in node neighborhoods. Furthermore, we incorporate the metric into the classical graph convolutional network (GCN) architecture and propose \textbf{N}eighborhood \textbf{H}omophily-based \textbf{G}raph \textbf{C}onvolutional \textbf{N}etwork (\textbf{NHGCN}). In this framework, neighbors are grouped by estimated \textit{NH} values and aggregated from different channels, and the resulting node predictions are then used in turn to estimate and update \textit{NH} values. The two processes of metric estimation and model inference are alternately optimized to achieve better node classification. NHGCN achieves top overall performance on both homophilous and heterophilous benchmarks, with an improvement of up to 7.4\% compared to the current SOTA methods.Comment: Accepted by the 32nd ACM International Conference on Information and Knowledge Management (CIKM 2023

Sparse Graph Learning with Spectrum Prior for Deep Graph Convolutional Networks

A graph convolutional network (GCN) employs a graph filtering kernel tailored for data with irregular structures. However, simply stacking more GCN layers does not improve performance; instead, the output converges to an uninformative low-dimensional subspace, where the convergence rate is characterized by the graph spectrum -- this is the known over-smoothing problem in GCN. In this paper, we propose a sparse graph learning algorithm incorporating a new spectrum prior to compute a graph topology that circumvents over-smoothing while preserving pairwise correlations inherent in data. Specifically, based on a spectral analysis of multilayer GCN output, we derive a spectrum prior for the graph Laplacian matrix $\mathbf{L}$ to robustify the model expressiveness against over-smoothing. Then, we formulate a sparse graph learning problem with the spectrum prior, solved efficiently via block coordinate descent (BCD). Moreover, we optimize the weight parameter trading off the fidelity term with the spectrum prior, based on data smoothness on the original graph learned without spectrum manipulation. The output $\mathbf{L}$ is then normalized for supervised GCN training. Experiments show that our proposal produced deeper GCNs and higher prediction accuracy for regression and classification tasks compared to competing schemes

Prediction of CO2\textrm{CO}_2 Adsorption in Nano-Pores with Graph Neural Networks

We investigate the graph-based convolutional neural network approach for predicting and ranking gas adsorption properties of crystalline Metal-Organic Framework (MOF) adsorbents for application in post-combustion capture of $\textrm{CO}_2$. Our model is based solely on standard structural input files containing atomistic descriptions of the adsorbent material candidates. We construct novel methodological extensions to match the prediction accuracy of classical machine learning models that were built with hundreds of features at much higher computational cost. Our approach can be more broadly applied to optimize gas capture processes at industrial scale.Comment: AAAI Conference on Artificial Intelligence (2022

A Study on Knowledge Graph Embeddings and Graph Neural Networks for Web Of Things

Graph data structures are widely used to store relational information between several entities. With data being generated worldwide on a large scale, we see a significant growth in the generation of knowledge graphs. Thing in the future is Orange's take on a knowledge graph in the domain of the Web Of Things (WoT), where the main objective of the platform is to provide a digital representation of the physical world and enable cross-domain applications to be built upon this massive and highly connected graph of things. In this context, as the knowledge graph grows in size, it is prone to have noisy and messy data. In this paper, we explore state-of-the-art knowledge graph embedding (KGE) methods to learn numerical representations of the graph entities and, subsequently, explore downstream tasks like link prediction, node classification, and triple classification. We also investigate Graph neural networks (GNN) alongside KGEs and compare their performance on the same downstream tasks. Our evaluation highlights the encouraging performance of both KGE and GNN-based methods on node classification, and the superiority of GNN approaches in the link prediction task. Overall, we show that state-of-the-art approaches are relevant in a WoT context, and this preliminary work provides insights to implement and evaluate them in this context

Deepened Graph Auto-Encoders Help Stabilize and Enhance Link Prediction

Graph neural networks have been used for a variety of learning tasks, such as link prediction, node classification, and node clustering. Among them, link prediction is a relatively under-studied graph learning task, with current state-of-the-art models based on one- or two-layer of shallow graph auto-encoder (GAE) architectures. In this paper, we focus on addressing a limitation of current methods for link prediction, which can only use shallow GAEs and variational GAEs, and creating effective methods to deepen (variational) GAE architectures to achieve stable and competitive performance. Our proposed methods innovatively incorporate standard auto-encoders (AEs) into the architectures of GAEs, where standard AEs are leveraged to learn essential, low-dimensional representations via seamlessly integrating the adjacency information and node features, while GAEs further build multi-scaled low-dimensional representations via residual connections to learn a compact overall embedding for link prediction. Empirically, extensive experiments on various benchmarking datasets verify the effectiveness of our methods and demonstrate the competitive performance of our deepened graph models for link prediction. Theoretically, we prove that our deep extensions inclusively express multiple polynomial filters with different orders.Comment: 10 page