相关论文: Spectral Convergence of Complexon Shift Operators

Simplicial complexes constitute the underlying topology of interacting complex systems including among the others brain and social interaction networks. They are generalized network structures that allow to go beyond the framework of…

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…

Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d…

Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to…

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…

In this work, we study the properties of sampling sets on families of large graphs by leveraging the theory of graphons and graph limits. To this end, we extend to graphon signals the notion of removable and uniqueness sets, which was…

Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…

The paper presents the graph signal processing (GSP) companion model that naturally replicates the basic tenets of classical signal processing (DSP) for GSP. The companion model shows that GSP can be made equivalent to DSP 'plus'…

Graph signal processing (GSP) generalizes signal processing (SP) tasks to signals living on non-Euclidean domains whose structure can be captured by a weighted graph. Graphs are versatile, able to model irregular interactions, easy to…

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

Weighing the topological domain over which data can be represented and analysed is a key strategy in many signal processing and machine learning applications, enabling the extraction and exploitation of meaningful data features and their…

We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces etc. To process…

Graphons, as limits of graph sequences, provide an operator-theoretic framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons induces convergence of the corresponding…

Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the…

This paper introduces topological Slepians, i.e., a novel class of signals defined over topological spaces (e.g., simplicial complexes) that are maximally concentrated on the topological domain (e.g., over a set of nodes, edges, triangles,…

We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via common faces and cofaces independently…

In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in $\mathbb{R}_+$. Here we show that by generalizing the classical definition of…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Due to their ability to model meaningful higher order relations among a set of entities, higher order network models have emerged recently as a powerful alternative for graph-based network models which are only capable of modeling binary…

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph…