I am a CNRS researcher in statistical signal processing and machine learning, currently with the GAIA (Geometrie Apprentissage Information et Algorithmes) team in the GIPSA laboratory, in Grenoble, French Alps.

*Research keywords:* graph signal processing, spectral clustering, sampling methods, determinantal point processes, random processes on graphs

# Internship positions

Internship positions are available on graph signal processing, determinantal point processes, community detection, machine learning. Please inquire by sending an e-mail at firstname.lastname [at] gipsa-lab.grenoble-inp.fr !# Current research interests

## Graph Tikhonov regularization and interpolation via random spanning forests

*denoising or interpolating a graph signal via random spanning forests*

## DPPs in the flat limit

*what happens to an L-ensemble when the kernel function tends to the flat limit?*

## Spectral Clustering in Sparse Graphs

*unifying methods from statistical physics, machine learning and statistics for the hard problem of spectral clustering in sparse graphs*

## Extended L-ensembles

*bridging the gap between L-ensembles and DPPs*

# Past research interests

## Determinantal Point Processes for Coresets

*efficiently creating summaries of large datasets that both preserve diversity and guarantee a low relative error for a given learning task*

## Revisiting the Bethe-Hessian: Improved Community Detection in Sparse Heterogeneous Graphs

*spectral clustering with the Bethe-Hessian: an improved parametrization to take into account heterogeneous degree distributions in sparse graphs*

## Asymptotic Equivalence of Fixed-size and Varying-size Determinantal Point Processes

*efficient and numerically stable approximate sampling of fixed-size DPP (so-called k-DPPs)*

## Determinantal Point Processes for Graph Sampling

*efficiently sampling bandlimited signals using repulsive point processes such as Determinantal Point Processes.*

## A Fast Graph Fourier Transform

*does the Graph Fourier Transform admit a O(NlogN) algorithm like the classical FFT?*

## Compressive Spectral Clustering

*combining graph signal processing
and compressed sensing to accelerate spectral clustering*

*compressive*spectral clustering method that accelerates the classical spectral clustering algorithm by bypassing the exact partial diagonalisation of the Laplacian of the similarity graph and the k-means step at high dimension. It can be summarised as follows:

1) generate a feature vector for each node by filtering O(log(k)) random Gaussian signals on G;

2) sample O(k log(k)) nodes from the full set of nodes;

3) cluster the reduced set of nodes;

4) interpolate the cluster indicator vectors back to the complete graph.

We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. Read more

## Random sampling of bandlimited signals on graphs

The goals here are both to reduce as much as possible the number of samples, while garanteeing robust reconstruction with respect to noise. We propose a random sampling strategy that meets these goals while sampling only O(klog(k)) nodes. Read more