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Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each…

Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning,…

Graph convolutional learning has led to many exciting discoveries in diverse areas. However, in some applications, traditional graphs are insufficient to capture the structure and intricacies of the data. In such scenarios, multigraphs…

Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph learning. As an essential part of spectral GNNs, spectral graph convolution extracts crucial frequency information in graph data, leading to superior…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph…

Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…

In the field of graph signal processing (GSP), directed graphs present a particular challenge for the "standard approaches" of GSP to due to their asymmetric nature. The presence of negative- or complex-weight directed edges, a graphical…

Graph Neural Networks (GNNs) typically operate by message-passing, where the state of a node is updated based on the information received from its neighbours. Most message-passing models act as graph convolutions, where features are mixed…

This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…

Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they…

In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…

Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…

Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this…

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be…

Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…

This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…

We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…