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Integrating the structural inductive biases of Graph Neural Networks (GNNs) with the global contextual modeling capabilities of Transformers represents a pivotal challenge in graph representation learning. While GNNs excel at capturing…

The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

The network embedding problem that maps nodes in a graph to vectors in Euclidean space can be very useful for addressing several important tasks on a graph. Recently, graph neural networks (GNNs) have been proposed for solving such a…

Sensing the fluid flow around an arbitrary geometry entails extrapolating from the physical quantities perceived at its surface in order to reconstruct the features of the surrounding fluid. This is a challenging inverse problem, yet one…

Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the…

Graph Fourier transform (GFT) is a fundamental concept in graph signal processing. In this paper, based on singular value decomposition of Laplacian, we introduce a novel definition of GFT on directed graphs, and use singular values of…

Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a…

In view of the huge success of convolution neural networks (CNN) for image classification and object recognition, there have been attempts to generalize the method to general graph-structured data. One major direction is based on spectral…

Rain streaks bring complicated pixel intensity changes and additional gradients, greatly obstructing the extraction of image features from background. This causes serious performance degradation in feature-based applications. Thus, it is…

Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…

Graph convolutional networks (GCNs) have achieved promising performance on various graph-based tasks. However they suffer from over-smoothing when stacking more layers. In this paper, we present a quantitative study on this observation and…

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…

Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…

Graph neural networks (GNNs) have revolutionized the field of machine learning on non-Euclidean data such as graphs and networks. GNNs effectively implement node representation learning through neighborhood aggregation and achieve…

Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…

Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts.…

Graph Neural Networks are powerful models for learning from graph-structured data, yet their effectiveness is often limited by two critical challenges: over-squashing, where information from distant nodes is excessively compressed, and…

Graph Neural Networks are powerful models for learning from graph-structured data, yet their effectiveness is often limited by two critical challenges: over-squashing, where information from distant nodes is excessively compressed, and…

With the development of deep convolutional neural networks, medical image segmentation has achieved a series of breakthroughs in recent years. However, the high-performance convolutional neural networks always mean numerous parameters and…