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Graphs are a central modeling tool for network-structured data. Depending on the application, the nodes of a graph may represent people in a social network, stations in a transportation network, web pages in the hyperlink network... basically any system made of interconnected sub-systems. Data on a graph, called graph signals, such as individual hobbies in a social network, or traffic at a given time in a transportation network, may typically be represented by a scalar per node. Processing these signals while taking into account the irregular structure on which they are defined is the goal of the young research field of Graph Signal Processing (GSP).

An important application of GSP is neuroscience data, where graphs are an essential modelisation tool of the brain at various scales of description. Also, the versatility of graphs made them popular for the processing (and even the joint processing) of many different types of brain signals: EEG, MEG, functional MRI, diffusion MRI...

**The objective of this conference day is two-fold:**

- a methodological perspective on recent advances in Graph Signal Processing. Topics of interest include: filtering, sampling, transforms, graph topology inference, higher-order graphs, learning over graphs, dynamic signals and/or dynamic graphs, etc.

- a focus on graphs for neuroscience data, with a special attention to cross-fertilize ideas from different scientific communities --neuroscience, network science and signal processing. How are graphs used today in neuroscience data processing? What are the needs in terms of methodological development? How can GSP bring new perspectives?

**Invited speakers:**

- Dimitri van de Ville (EPFL)

- Mahmoud Hassan (LTSI, Rennes)

- Sarah Morgan (Cambridge)

**Call for abstracts (oral presentations and posters)**

Everyone, and especially PhD students, are encouraged to participate and present their work at this conference day: please send an abstract (maximum 1 page) to the organizers **before the ****1st of September**** (extended to the 9th of September).**

**Where?**

The conference room of délégation CNRS (site d'Ivry-sur-Seine): 27 rue Paul Bert, 94204 Ivry sur Seine (subway 7, Paris). http://www.dr1.cnrs.fr/spip.php?article116

**When?**

Wednesday 25th of September 2019. All day.

**Organizers:**

- Nicolas Tremblay (Gipsa-lab, CNRS) : nicolas.tremblay@gipsa-lab.fr

- Bastien Pasdeloup (EPFL) : bastien.pasdeloup@gmail.com

This is the program for the day:

- 09h15: doors open

- 09h45: welcome talk

- 10h - 10h55 : D. van de Ville (EPFL), Graph Signal Processing for Human Neuroimaging Addresses Function-Structure Relationships

- 10h55 - 11h15 : Potel et al. (Rennes), Imaging disrupted brain networks at rest in Parkinson's disease using dense EEG

- 11h15 - 11h35 : Takerkart (Marseille, institut la Timone), Learning from individual parcellations using functionaly informed brain graphs

- 11h35 - 11h55 : Cattai et al. (Sorbonne Université), EEG network mechanisms in motor imagery-based BCI tasks

- 11h55 - 12h15 : Brahim and Farrugia (IMT Atlantique), Graph Fourier Transform of temporal fluctuations of brain activity for supervised learning

- 12h15 - 13h45 : lunch

- 13h45 - 14h40 : M. Hassan (Rennes), Tracking sub-second dynamic brain networks using electroencephalography

- 14h40 - 15h35 : S. Morgan (Cambridge), Applications of network neuroscience- in development, health and disease

- 15h35 - 15h50 : break

- 15h50 - 16h10 : Frusque et al. (ENS Lyon), Time Varying Graphical Lasso on Phase Synchronizing Time Series

- 16h10 - 16h30 : Melot et al. (Marseille), Intertwinning wavelets or multiresolution analysis on graphs through random forests.

- 16h30 - 16h50 : Keriven et al. (ENS Paris), Universal Invariant and Equivariant Graph Neural Networks

- 16h50 - 17h00 : Final words

State-of-the-art magnetic resonance imaging (MRI) provides unprecedented opportunities to study brain structure (anatomy) and function (physiology). Based on such data, graph representations can be built where nodes are associated to brain regions and edge weights to strengths of structural or functional connections. In particular, structural graphs capture major neural pathways in white matter, while functional graphs map out statistical interdependencies between pairs of regional activity traces. Network analysis of these graphs has revealed emergent system-level properties of brain structure or function, such as efficiency of communication and modular organization.

In this talk, graph signal processing (GSP) will be presented as a novel framework to integrate brain structure, contained in the structural graph, with brain function, characterized by activity traces that can be considered as time-dependent graph signals. Such a perspective allows to define novel meaningful graph-filtering operations of brain activity that take into account smoothness of signals on the anatomical backbone. For instance, we will show how activity can be analyzed in terms of being aligned versus liberal with respect to brain structure, or how additional prior information about cognitive systems can be incorporated. The well-known Fourier phase randomization method to generate surrogate data can also be adapted to this new setting. Finally, recent work will highlight how the spatial resolution of this type of analyses can be increased to the voxel level, representing a few ten thousands of nodes.

References:

W. Huang, T. A. W. Bolton, J. D. Medaglia, D. S. Bassett, A. Ribeiro & D. Van De Ville, « A Graph Signal Processing Perspective on Functional Brain Imaging », Proceedings of the IEEE, 2018, 106, 868-885

M. G. Preti, D. Van De Ville, « Decoupling of Brain Function from Structure Reveals Regional Behavioral Specialization in Humans », arXiv:1905.07813

Parkinson's disease (PD) is the second most frequent neurodegenerative pathology, concerning about 200000 patients in France. Cognitive impairment is a critical combination of symptoms that often affects parkinsonian patients. Fine assessment of these symptoms is highly needed to treat patients with the right therapeutics. Functional connectivity has recently been assessed in Parkinson's disease using dense EEG, within parkinsonian patients according to their cognitive status (Hassan et al., 2017). Thus, functional connectivity may be used as a biomarker in PD-related cognitive impairment. Here, I will present results concerning edge-wise and node-wise network disruptions between healthy controls and parkinsonian patients. We used the source connectivity method to compute cortical activity from dense EEG recordings and assessed graph theory measures. This early work is a first step in building a biomarker of cognitive impairment in PD using dense EEG.

The fast development of modern neuroimaging techniques provides neuroscientists with unprecedented opportunities to improve their understanding of the organization of the brain. In particular, machine learning methods allow for the development of models that can predict characteristics of individual subjects, either linked to their behavior or their clinical state. Designing such predictive models remains challenging because of the complex nature of the data, its high-dimensionality and the strong differences that exist between individuals. This emphasizes the need for effective representations based on individual data and for learning methods that exploits knowledge about inter-individual variability. In this paper, we precisely describe a generic framework that allows obtaining accurate predictive models by answering these two needs. First, the neuroimaging data is segmented to obtain a parcellation which is then represented as an attributed graph. Secondly, such graphical representations are compared using a graph kernel that embeds a model of inter-individual variability, allowing to exploit the large array of available kernel methods in order to perform predictions on data from new individuals. We demonstrate the genericity of this framework by describing three applications, respectively on functional, anatomical and diffusion magnetic resonance imaging data, where the proposed method either answers new questions and/or outperforms existing methods.

Abstract soon available

Previous work on Graph Signal Processing (GSP) applied to neuroimaging data has mainly focused on deriving useful statistical descriptors for analyzing and interpreting brain activity, such as smoothness or spectral power in the graph fourier domain. Other studies have attempted at exploiting GSP to decode brain activity, by extracting feature vectors for supervised learning, using either graph fourier transform or spectral graph wavelet transform. The previous contributions have all considered either averaged brain activity, as summarized by a first level linear model (so called beta maps, as in [3]), or GSP metrics calculated at each time step. In this presentation, after quickly summarizing our previous work on combining GSP and machine learning, we will test the idea whether incorporating anatomical dependencies between brain regions using a structural graph can restore information content from several temporal statistics of brain activity. More specifically, the resting state functional magnetic resonance imaging (rs-fMRI) time series of each brain subject are characterized by several statistical metrics. Then, these measures are projected on a structural graph, which is computed from a healthy brain structural connectivity of the human connectome project.Further analysis shows that the combination of the structural connectivity with the standard deviation of fMRI temporal signals can lead to more accurate supervised classification for 172 subjects from the biggest site of the Autism Brain Imaging Data Exchange (ABIDE) datasets. Moreover, the proposed approach outperforms several approaches, based on using functional connectome or complex functional network measures.

The human brain is a large-scale network (graph) the function of which depends on dynamic communications (edges) between spatially distributed regions (nodes). Magneto/electro-encephalography (M/EEG) provides a unique direct and noninvasive access to the electrophysiological activity of the whole brain, at the millisecond scale. In this talk, I will introduce emergent methods used to track the cortical network dynamics, through M/EEG sensors, at rest and task. I will discuss the potential use of these methods to address some present and future cognitive and clinical neuroscience questions.

The brain can be thought of as a highly complex network, whose intricate structure and dynamics span multiple temporal and spatial scales. Whilst we are unable to map this network at the neuronal level, MRI brain imaging gives us an invaluable window into macroscopic brain connectivity. For example, MRI brain networks have been used to study the developmental changes that happen during childhood and adolescence (Whitaker and Vertes, PNAS 2016), as well as the biological underpinnings of schizophrenia (Morgan et al, PNAS 2019). In this talk I will showcase a few examples of how MRI brain networks can shed light on the human brain in development, health and disease. I will describe how the networks can be derived (including work using a new technique known as morphometric similarity mapping- Seidlitz et al, Neuron 2018), analysed and ultimately what insights they give us. I will finish by briefly describing how we can link these macroscopic brain networks to openly available gene expression data from the Allen Human Brain Atlas. This approach takes us back to the microscale and can provide important clues as to the biological mechanisms underlying our results.

We consider the problem of inferring the conditional independence graph from the partial phase locking value index (pPLV) of multivariate time series. A typical application is: the inference of temporal functional connectivity from brain data. We propose to extend the recently proposed time-varying graphical lasso to the measure of partial locking value, resulting in a sparse and a temporally coherent dynamical graph, characterizing the evolution of the phase synchrony between each pair of signals. Two methods are proposed: using a non parametric estimate of the phase locking value, or assuming recorded signals locally follow a multivariate Gaussian distribution. We solve this optimization problem using the alternating direction method of multiplier. We validate our approach and compare both methods in simulation using Roessler oscillators and with a real iEEG dataset from an epileptic patient.

In this communication we propose the construction of a multiresolution wavelet basis on graphs. The construction relies on a random spanning forest to provide a downsampling set, and on approximate solutions of Markov intertwining equation to provide a subgraph structure. Even if the basis functions are well localized, they are not orthonormal but we have an explicit reconstruction formula. Furthermore a Jackson-like inequality garantees that whenever the signal is smooth (with a small laplacian) it can be well approximated using only the scaling functions of the basis. We illustrate the method by numerical experiments computed with the Python Package IntertwiningWavelet developped by Dominique Benielli (Labex Archimède, Université Aix-Marseille) to process the method.

Graph Neural Networks (GNN) come in many flavors, but should always be either invariant (permutation of the nodes of the input graph does not affect the output) or equivariant (permutation of the input permutes the output). In this paper, we consider a specific class of invariant and equivariant networks, for which we prove new universality theorems. Recently, Maron et al. (2019) showed that by allowing higher-order tensorization inside the network, universal invariant GNNs can be obtained. As a first contribution, we propose an alternative proof of this result, which relies on the Stone-Weierstrass theorem for algebra of real-valued functions. Our main contribution is then an extension of this result to the equivariant case. The proof relies on a new generalized Stone-Weierstrass theorem for algebra of equivariant functions, which is of independent interest. This is joint work with Gabriel Peyré (ENS).

**Date :** 2019-09-25

**Lieu :** Salle de conférence de la délégation CNRS Paris-Villejuif - Site d?Ivry-sur-Seine

**Thèmes scientifiques :**

A - Méthodes et modèles en traitement de signal

**Inscriptions closes à cette réunion.**

(c) GdR 720 ISIS - CNRS - 2011-2020.