Graph convolutional networks with multi-level coarsening for graph classification

Graph Geometric Algebra networks for graph representation learning

Graph neural networks (GNNs) have emerged as a prominent approach for capturing graph topology and modeling vertex-to-vertex relationships. They have been widely used in pattern recognition tasks including node and graph label prediction. However, when dealing with graphs from non-Euclidean domains, the relationships, and interdependencies between objects become more complex. Existing GNNs face limitations in handling a large number of model parameters in such complex graphs. To address this, we propose the integration of Geometric Algebra into graph neural networks, enabling the generalization of GNNs within the geometric space to learn geometric embeddings for nodes and graphs. Our proposed Graph Geometric Algebra Network (GGAN) enhances correlations among nodes by leveraging relations within the Geometric Algebra space. This approach reduces model complexity and improves the learning of graph representations. Through extensive experiments on various benchmark datasets, we demonstrate that our models, utilizing the properties of Geometric Algebra operations, outperform state-of-the-art methods in graph classification and semi-supervised node classification tasks. Our theoretical findings are empirically validated, confirming that our model achieves state-of-the-art performance.

Understanding Pooling in Graph Neural Networks

Many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. In this article, we present an operational framework to unify this vast and diverse literature by describing pooling operators as the combination of three functions: selection, reduction, and connection (SRC). We then introduce a taxonomy of pooling operators, based on some of their key characteristics and implementation differences under the SRC framework. Finally, we propose three criteria to evaluate the performance of pooling operators and use them to investigate the behavior of different operators on a variety of tasks.

Ridge-Regression-Induced Robust Graph Relational Network

Graph convolutional networks (GCNs) have attracted increasing research attention, which merits in its strong ability to handle graph data, such as the citation network or social network. Existing models typically use first-order neighborhood information to design specific convolution operations, which aggregate the features of all adjacent nodes. However, such models ignore the high-order spatial relationship among neighboring nodes in noisy data due to its modeling complexity. In this article, we propose a novel robust graph relational network to address this issue toward modeling high-order relationships in noisy data for graph convolution. Our key innovation lies in designing a generic relation network layer, which is used to infer the underlying relations among adjacent noisy nodes. Specifically, a fixed number of adjacent nodes for each node is chosen by solving the ridge regression problem, in which the regression coefficients are used to rank the adjacent nodes of each node in a graph. Furthermore, to mine the rich features, we extract high-order information from the nodes to significantly enhance the representation ability of the GCNs for extensive applications. We conduct extensive semisupervised node classification experiments on the noisy benchmark datasets, which clearly show that our model is superior to the existing methods and can achieve state-of-the-art performance.

Are Graph Convolutional Networks With Random Weights Feasible?

Graph Convolutional Networks (GCNs), as a prominent example of graph neural networks, are receiving extensive attention for their powerful capability in learning node representations on graphs. There are various extensions, either in sampling and/or node feature aggregation, to further improve GCNs' performance, scalability and applicability in various domains. Still, there is room for further improvements on learning efficiency because performing batch gradient descent using the full dataset for every training iteration, as unavoidable for training (vanilla) GCNs, is not a viable option for large graphs. The good potential of random features in speeding up the training phase in large-scale problems motivates us to consider carefully whether GCNs with random weights are feasible. To investigate theoretically and empirically this issue, we propose a novel model termed Graph Convolutional Networks with Random Weights (GCN-RW) by revising the convolutional layer with random filters and simultaneously adjusting the learning objective with regularized least squares loss. Theoretical analyses on the model's approximation upper bound, structure complexity, stability and generalization, are provided with rigorous mathematical proofs. The effectiveness and efficiency of GCN-RW are verified on semi-supervised node classification task with several benchmark datasets. Experimental results demonstrate that, in comparison with some state-of-the-art approaches, GCN-RW can achieve better or matched accuracies with less training time cost.

DFinder: a novel end-to-end graph embedding-based method to identify drug-food interactions

MOTIVATION

Drug-food interactions (DFIs) occur when some constituents of food affect the bioaccessibility or efficacy of the drug by involving in drug pharmacodynamic and/or pharmacokinetic processes. Many computational methods have achieved remarkable results in link prediction tasks between biological entities, which show the potential of computational methods in discovering novel DFIs. However, there are few computational approaches that pay attention to DFI identification. This is mainly due to the lack of DFI data. In addition, food is generally made up of a variety of chemical substances. The complexity of food makes it difficult to generate accurate feature representations for food. Therefore, it is urgent to develop effective computational approaches for learning the food feature representation and predicting DFIs.

RESULTS

In this article, we first collect DFI data from DrugBank and PubMed, respectively, to construct two datasets, named DrugBank-DFI and PubMed-DFI. Based on these two datasets, two DFI networks are constructed. Then, we propose a novel end-to-end graph embedding-based method named DFinder to identify DFIs. DFinder combines node attribute features and topological structure features to learn the representations of drugs and food constituents. In topology space, we adopt a simplified graph convolution network-based method to learn the topological structure features. In feature space, we use a deep neural network to extract attribute features from the original node attributes. The evaluation results indicate that DFinder performs better than other baseline methods.

AVAILABILITY AND IMPLEMENTATION

The source code is available at https://github.com/23AIBox/23AIBox-DFinder.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Sex Differences of Cerebellum and Cerebrum: Evidence from Graph Convolutional Network

This work aims to exploit a novel graph neural network to predict the sex of the brain topological network, and to find the sex differences in the cerebrum and cerebellum. A two-branch multi-scale graph convolutional network (TMGCN) is designed to analyze the sex differences of the brain. Two complementary templates are used to construct cerebrum and cerebellum networks, respectively, followed by a two-branch sub-network with multi-scale filters and a trainable weighted fusion strategy for the final prediction. Finally, a trainable graph topk-pooling layer is utilized in our model to visualize key brain regions relevant to the prediction. The proposed TMGCN achieves a prediction accuracy of 84.48%. In the cerebellum, the bilateral Crus I-II, lobule VI and VIIb, and the posterior vermis (VI-X) are discriminative for this task. As for the cerebrum, the discriminative brain regions consist of the bilateral inferior temporal gyrus, the bilateral fusiform gyrus, the bilateral parahippocampal gyrus, the bilateral cingulate gyrus, the bilateral medial ventral occipital cortex, the bilateral lateral occipital cortex, the bilateral amygdala, and the bilateral hippocampus. This study tackles the sex prediction problem from a more comprehensive view, and may provide the resting-state fMRI evidence for further study of sex differences in the cerebellum and cerebrum.