Related papers: On distributional graph signals
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…
Movie graphs play an important role to bridge heterogenous modalities of videos and texts in human-centric retrieval. In this work, we propose Graph Wasserstein Correlation Analysis (GWCA) to deal with the core issue therein, i.e, cross…
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…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
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…
This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an…
In this paper we state the basics for a signal processing framework on quiver representations. A quiver is a directed graph and a quiver representation is an assignment of vector spaces to the nodes of the graph and of linear maps between…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e. a set of points along with a set of neighborhood relations. This setup does not require the definition of a metric and…
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…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…
In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
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…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
Signal processing on graphs is a recent research domain that aims at generalizing classical tools in signal processing, in order to analyze signals evolving on complex domains. Such domains are represented by graphs, for which one can…