Related papers: Introducing Hypergraph Signal Processing: Theoreti…
In the past years, many signal processing operations have been successfully adapted to the graph setting. One elegant and effective approach is to exploit the eigendecomposition of a graph shift operator (GSO), such as the adjacency or…
Graph signals are widely used to describe vertex attributes or features in graph-structured data, with applications spanning the internet, social media, transportation, sensor networks, and biomedicine. Graph signal processing (GSP) has…
Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel…
In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.
Graphs are irregular structures which naturally account for data integrity, however, traditional approaches have been established outside Signal Processing, and largely focus on analyzing the underlying graphs rather than signals on graphs.…
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph…
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more…
Wireless sensor networks (WSNs) are considered as a major technology enabling the Internet of Things (IoT) paradigm. The recent emerging Graph Signal Processing field can also contribute to enabling the IoT by providing key tools, such as…
Graphs are widely used to encapsulate a variety of data formats, but real-world networks often involve complex node relations beyond only being pairwise. While hypergraphs and hierarchical graphs have been developed and employed to account…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
Last decade has seen the emergence of numerous methods for learning on graphs, particularly Graph Neural Networks (GNNs). These methods, however, are often not directly applicable to more complex structures like bipartite graphs (equivalent…
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…
Recently, graph neural networks have been widely used for network embedding because of their prominent performance in pairwise relationship learning. In the real world, a more natural and common situation is the coexistence of pairwise…
Our goal in this paper is to leverage the potential of the topological signal processing (TSP) framework for analyzing brain networks. Representing brain data as signals over simplicial complexes allows us to capture higher-order…
The first step for any graph signal processing (GSP) procedure is to learn the graph signal representation, i.e., to capture the dependence structure of the data into an adjacency matrix. Indeed, the adjacency matrix is typically not known…
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…
Signal processing is crucial for satisfying the high data rate requirements of future sixth-generation (6G) wireless networks. However, the rapid growth of wireless networks has brought about massive data traffic, which hinders the…
Recent progress in graph signal processing (GSP) has addressed a number of problems, including sampling and filtering. Proposed methods have focused on generic graphs and defined signals with certain characteristics, e.g., bandlimited…