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GOT: An Optimal Transport framework for Graph comparison

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Community-Aware Graph Signal Processing: Modularity Defines New Ways of Processing Graph Signals

Dimitri Nestor Alice Van De Ville, Thomas William Arthur Bolton, Raphaël Pierre Liégeois

The emerging field of graph signal processing (GSP) allows one 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 in studying ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Online Distributed Learning Over Graphs With Multitask Graph-Filter Models

Ali H. Sayed, Roula Nassif

In this article, we are interested in adaptive and distributed estimation of graph filters from streaming data. We formulate this problem as a consensus estimation problem over graphs, which can be addressed with diffusion LMS strategies. Most popular grap ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Graph Laplacians for Rotation Equivariant Convolutional Neural Networks

Martino Milani

A fundamental problem in signal processing is to design computationally efficient algorithms to filter signals. In many applications, the signals to filter lie on a sphere. Meaningful examples of data of this kind are weather data on the Earth, or images o ...

2019

Slepian Guided Filtering of Graph Signals

Dimitri Nestor Alice Van De Ville, Miljan Petrovic

Joint localization of graph signals in vertex and spectral domain is achieved in Slepian vectors calculated by either maximizing energy concentration (mu) or minimizing modified embedded distance (xi) in the subgraph of interest. On the other hand, graph L ...

SPIE-INT SOC OPTICAL ENGINEERING2019

Incidences Between Planes Over Finite Fields

In this note, we use methods from spectral graph theory to obtain bounds on the number of incidences between k-planes and h-planes in F-q(d), which generalizes a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove tha ...

AMER MATHEMATICAL SOC2019

Spectrally approximating large graphs with smaller graphs

Pierre Vandergheynst, Andreas Loukas

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...

2018

Robust and Efficient Data Clustering with Signal Processing on Graphs

Lionel Jérémie Martin

Data is pervasive in today's world and has actually been for quite some time. With the increasing volume of data to process, there is a need for faster and at least as accurate techniques than what we already have. In particular, the last decade recorded t ...

EPFL2018

Filtering Random Graph Processes Over Random Time-Varying Graphs

Andreas Loukas

Graph filters play a key role in processing the graph spectra of signals supported on the vertices of a graph. However, despite their widespread use, graph filters have been analyzed only in the deterministic setting, ignoring the impact of stochasticity i ...

Institute of Electrical and Electronics Engineers2017

Graph learning under sparsity priors

Pascal Frossard, Hermina Petric Maretic

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. ...

Ieee2017

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Robin Jonathan Demesmaeker

The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smalles ...

Institute of Electrical and Electronics Engineers2017