Related papers: Abstract message passing and distributed graph sig…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of…
The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets,…
Graph processing has become an important part of various areas of computing, including machine learning, medical applications, social network analysis, computational sciences, and others. A growing amount of the associated graph processing…
This tutorial paper refers to the use of graph-theoretic concepts for analyzing brain signals. For didactic purposes it splits into two parts: theory and application. In the first part, we commence by introducing some basic elements from…
This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the…
Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks,…
The trust in the predictions of Graph Neural Networks is limited by their opaque reasoning process. Prior methods have tried to explain graph networks via concept-based explanations extracted from the latent representations obtained after…
We establish connections between the Transformer architecture, originally introduced for natural language processing, and Graph Neural Networks (GNNs) for representation learning on graphs. We show how Transformers can be viewed as message…
Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and…
We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
Designing distributed optimal controllers subject to communication constraints is a difficult problem unless structural assumptions are imposed on the underlying dynamics and information exchange structure, e.g., sparsity, delay, or spatial…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…