Related papers: Topological Signal Processing over Generalized Cel…
We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not…
Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…
Temporal graph signals are multivariate time series with individual components associated with nodes of a fixed graph structure. Data of this kind arises in many domains including activity of social network users, sensor network readings…
Graph-based recommender systems have achieved remarkable effectiveness by modeling high-order interactions between users and items. However, such approaches are significantly undermined by popularity bias, which distorts the interaction…
This paper studies semi-supervised graph classification, a crucial task with a wide range of applications in social network analysis and bioinformatics. Recent works typically adopt graph neural networks to learn graph-level representations…
The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology…
Graph signal processing (GSP) studies graph-structured data, where the central concept is the vector space of graph signals. To study a vector space, we have many useful tools up our sleeves. However, uncertainty is omnipresent in practice,…
The application of graph signal processing (GSP) on partially observed graph signals with missing nodes has gained attention recently. This is because processing data from large graphs are difficult, if not impossible due to the lack of…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the…
Modern neuroimaging techniques provide us with unique views on brain structure and function; i.e., how the brain is wired, and where and when activity takes place. Data acquired using these techniques can be analyzed in terms of its network…
The underlying theme of this paper is to explore the various facets of power systems data through the lens of graph signal processing (GSP), laying down the foundations of the Grid-GSP framework. Grid-GSP provides an interpretation for the…
Graphons are limit objects of sequences of graphs and are used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study signal processing on large graphs. A major limitation of this approach…
Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…
In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we…
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…
This document introduces the Graph Signal Processing Toolbox (GSPBox) a framework that can be used to tackle graph related problems with a signal processing approach. It explains the structure and the organization of this software. It also…
On the Euclidean domains of classical signal processing, linking of signal samples to the underlying coordinate structure is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying…
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…
Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been…