Related papers: Topological Signal Processing over Simplicial Comp…
The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role…
Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…
Signal processing over single-layer graphs has become a mainstream tool owing to its power in revealing obscure underlying structures within data signals. However, many real-life datasets and systems, {including those in Internet of Things…
The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph…
As irregularly structured data representations, graphs have received a large amount of attention in recent years and have been widely applied to various real-world scenarios such as social, traffic, and energy settings. Compared to…
Deep learning, particularly convolutional neural networks (CNNs), have yielded rapid, significant improvements in computer vision and related domains. But conventional deep learning architectures perform poorly when data have an underlying…
Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains…
Signal processing over graphs has recently attracted significant attentions for dealing with structured data. Normal graphs, however, only model pairwise relationships between nodes and are not effective in representing and capturing some…
Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to…
In this tutorial, we provide a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on…
Topological Signal Processing (TSP) utilizes simplicial complexes to model structures with higher order than vertices and edges. In this paper, we study the transferability of TSP via a generalized higher-order version of graphon, known as…
Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph…
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to…
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…
Graph signal processing (GSP) has become an important tool in many areas such as image processing, networking learning and analysis of social network data. In this paper, we propose a broader framework that not only encompasses traditional…
Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil new fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are…
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…
Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…
Graph signal processing (GSP) deals with the representation, analysis, and processing of structured data, i.e. graph signals that are defined on the vertex set of a generic graph. A crucial prerequisite for applying various GSP and graph…
Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on…