Related papers: Interpretable Stability Bounds for Spectral Graph …

We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…

Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their…

Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…

Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

Network data can be conveniently modeled as a graph signal, where data values are assigned to the nodes of a graph describing the underlying network topology. Successful learning from network data requires methods that effectively exploit…

Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…

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…

When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…

When approaching graph signal processing tasks, graphs are usually assumed to be perfectly known. However, in many practical applications, the observed (inferred) network is prone to perturbations which, if ignored, will hinder performance.…

Graph Neural Networks (GNNs) have achieved remarkable success in various graph-based learning tasks. While their performance is often attributed to the powerful neighborhood aggregation mechanism, recent studies suggest that other…

Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…

With recent advancements in graph neural networks (GNNs), spectral GNNs have received increasing popularity by virtue of their ability to retrieve graph signals in the spectral domain. These models feature uniqueness in efficient…

We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is…

Graph Neural Networks (GNNs) show impressive performance in many practical scenarios, which can be largely attributed to their stability properties. Empirically, GNNs can scale well on large size graphs, but this is contradicted by the fact…

Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…

Spectral graph neural networks (GNNs) learn graph representations via spectral-domain graph convolutions. However, most existing spectral graph filters are scalar-to-scalar functions, i.e., mapping a single eigenvalue to a single filtered…

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from graph-structured data. However, even state-of-the-art architectures have limitations on what structures they can distinguish, imposing theoretical limits on what…

Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…

Graph filtering is the cornerstone operation in graph signal processing (GSP). Thus, understanding it is key in developing potent GSP methods. Graph filters are local and distributed linear operations, whose output depends only on the local…