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Many applications in pattern recognition represent patterns as a geometric graph. The geometric graph distance (GGD) has recently been studied as a meaningful measure of similarity between two geometric graphs. Since computing the GGD is…

We analyze the universality and generalization of graph neural networks (GNNs) on attributed graphs, i.e., with node attributes. To this end, we propose pseudometrics over the space of all attributed graphs that describe the fine-grained…

Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a…

How can we subsample graph data so that a graph neural network (GNN) trained on the subsample achieves performance comparable to training on the full dataset? This question is of fundamental interest, as smaller datasets reduce labeling…

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…

Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the vertices of a graph. They are built from layers of graph convolutions which serve as a powerful…

This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to…

Graph Neural Networks (GNNs) have shown great power in various domains. However, their predictions may inherit societal biases on sensitive attributes, limiting their adoption in real-world applications. Although many efforts have been…

Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…

Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information…

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has…

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Graph structured data, specifically text-attributed graphs (TAG), effectively represent relationships among varied entities. Such graphs are essential for semi-supervised node classification tasks. Graph Neural Networks (GNNs) have emerged…

The dominant paradigm for machine learning on graphs uses Message Passing Graph Neural Networks (MP-GNNs), in which node representations are updated by aggregating information in their local neighborhood. Recently, there have been…

The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…

Despite much research, Graph Neural Networks (GNNs) still do not display the favorable scaling properties of other deep neural networks such as Convolutional Neural Networks and Transformers. Previous work has identified issues such as…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

Local neighborhoods play a crucial role in embedding generation in graph-based learning. It is commonly believed that nodes ought to have embeddings that resemble those of their neighbors. In this research, we try to carefully expand the…

Graph Neural Networks (GNNs) have achieved significant success in learning better representations by performing feature propagation and transformation iteratively to leverage neighborhood information. Nevertheless, iterative propagation…