arXiv subjects

Pierre Borgnat

Publications and source records attributed to Pierre Borgnat.

At least 19 recordsLinked to original sources

arXiv2026

Inverse Laplace Transform for Dynamic Light Scattering: Impact of Regularization

Dynamic Light Scattering (DLS) analyzes particle dynamics from the autocorrelation functions of scattered light intensity, yet extracting accurate relaxation time distributions from noisy data is challenging. We develop an inverse problem approach to recover this distribution by inverting the Laplace transform with physics-based regularization, called the CONTIN method. We improve it to use it on noisy data, across a wide range of time scales, with a selection of the regularization strength through a data-driven L-curve criterion. Our approach enhances robustness under high noise and reveals multi-scale dynamics in complex systems. Validation is performed on simulated data, compared to the Cram\'er-Rao bound and to parametric methods, and on experimental data from Carbopol microgels. It demonstrates superior accuracy over parametric methods, especially for broad time distributions. The algorithm's logarithmic discretization and variance-reduced correlation estimation enhance performance, offering a powerful tool for non-parametric DLS analysis and deeper insights into soft matter dynamics.

cond-mat.soft↗

arXiv2024

PASCO (PArallel Structured COarsening): an overlay to speed up graph clustering algorithms

Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spectral clustering requires the computation of the spectral decomposition of the Laplacian matrix, which is not applicable for large graphs with a large number of communities. This work introduces PASCO, an overlay that accelerates clustering algorithms. Our method consists of three steps: 1-We compute several independent small graphs representing the input graph by applying an efficient and structure-preserving coarsening algorithm. 2-A clustering algorithm is run in parallel onto each small graph and provides several partitions of the initial graph. 3-These partitions are aligned and combined with an optimal transport method to output the final partition. The PASCO framework is based on two key contributions: a novel global algorithm structure designed to enable parallelization and a fast, empirically validated graph coarsening algorithm that preserves structural properties. We demonstrate the strong performance of 1 PASCO in terms of computational efficiency, structural preservation, and output partition quality, evaluated on both synthetic and real-world graph datasets.

cs.LG↗

arXiv2024

Longitudinal Modularity, a Modularity for Link Streams

Temporal networks are commonly used to model real-life phenomena. When these phenomena represent interactions and are captured at a fine-grained temporal resolution, they are modeled as link streams. Community detection is an essential network analysis task. Although many methods exist for static networks, and some methods have been developed for temporal networks represented as sequences of snapshots, few works can handle link streams. This article introduces the first adaptation of the well-known Modularity quality function to link streams. Unlike existing methods, it is independent of the time scale of analysis. After introducing the quality function, and its relation to existing static and dynamic definitions of Modularity, we show experimentally its relevance for dynamic community evaluation.

cs.SI↗

arXiv2024

A Comparative Analysis of Gene Expression Profiling by Statistical and Machine Learning Approaches

Many machine learning models have been proposed to classify phenotypes from gene expression data. In addition to their good performance, these models can potentially provide some understanding of phenotypes by extracting explanations for their decisions. These explanations often take the form of a list of genes ranked in order of importance for the predictions, the highest-ranked genes being interpreted as linked to the phenotype. We discuss the biological and the methodological limitations of such explanations. Experiments are performed on several datasets gathering cancer and healthy tissue samples from the TCGA, GTEx and TARGET databases. A collection of machine learning models including logistic regression, multilayer perceptron, and graph neural network are trained to classify samples according to their cancer type. Gene rankings are obtained from explainability methods adapted to these models, and compared to the ones from classical statistical feature selection methods such as mutual information, DESeq2, and EdgeR. Interestingly, on simple tasks, we observe that the information learned by black-box neural networks is related to the notion of differential expression. In all cases, a small set containing the best-ranked genes is sufficient to achieve a good classification. However, these genes differ significantly between the methods and similar classification performance can be achieved with numerous lower ranked genes. In conclusion, although these methods enable the identification of biomarkers characteristic of certain pathologies, our results question the completeness of the selected gene sets and thus of explainability by the identification of the underlying biological processes.

q-bio.GN↗

arXiv2023

Mosaic benchmark networks: Modular link streams for testing dynamic community detection algorithms

Community structure is a critical feature of real networks, providing insights into nodes' internal organization. Nowadays, with the availability of highly detailed temporal networks such as link streams, studying community structures becomes more complex due to increased data precision and time sensitivity. Despite numerous algorithms developed in the past decade for dynamic community discovery, assessing their performance on link streams remains a challenge. Synthetic benchmark graphs are a well-accepted approach for evaluating static community detection algorithms. Additionally, there have been some proposals for slowly evolving communities in low-resolution temporal networks like snapshots. Nevertheless, this approach is not yet suitable for link streams. To bridge this gap, we introduce a novel framework that generates synthetic modular link streams with predefined communities. Subsequently, we evaluate established dynamic community detection methods to uncover limitations that may not be evident in snapshots with slowly evolving communities. While no method emerges as a clear winner, we observe notable differences among them.

cs.SI↗

arXiv2023

Temporal network compression via network hashing

Pairwise temporal interactions between entities can be represented as temporal networks, which code the propagation of processes such as epidemic spreading or information cascades, evolving on top of them. The largest outcome of these processes is directly linked to the structure of the underlying network. Indeed, a node of a network at given time cannot affect more nodes in the future than it can reach via time-respecting paths. This set of nodes reachable from a source defines an out-component, which identification is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms other state-of-the-art methods. Secondly, we propose a hashing framework to coarsen large temporal networks into smaller proxies on which out-components are easier to estimate, and then recombined to obtain the initial components. Our graph hashing solution has implications in privacy respecting representation of temporal networks.

cs.SI↗

arXiv2023

Studying Limits of Explainability by Integrated Gradients for Gene Expression Models

Understanding the molecular processes that drive cellular life is a fundamental question in biological research. Ambitious programs have gathered a number of molecular datasets on large populations. To decipher the complex cellular interactions, recent work has turned to supervised machine learning methods. The scientific questions are formulated as classical learning problems on tabular data or on graphs, e.g. phenotype prediction from gene expression data. In these works, the input features on which the individual predictions are predominantly based are often interpreted as indicative of the cause of the phenotype, such as cancer identification. Here, we propose to explore the relevance of the biomarkers identified by Integrated Gradients, an explainability method for feature attribution in machine learning. Through a motivating example on The Cancer Genome Atlas, we show that ranking features by importance is not enough to robustly identify biomarkers. As it is difficult to evaluate whether biomarkers reflect relevant causes without known ground truth, we simulate gene expression data by proposing a hierarchical model based on Latent Dirichlet Allocation models. We also highlight good practices for evaluating explanations for genomics data and propose a direction to derive more insights from these explanations.

q-bio.GN↗

arXiv2023

Clustering with Simplicial Complexes

In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on minimizing, yields an optimal partition with a higher density of filled triangles within the set while the density of filled triangles is smaller across the sets. To this end, we propose a simplicial adjacency operator that captures the relation between the nodes through second-order simplices. This allows us to extend the well-known Cheeger inequality to cluster a simplicial complex. Then, leveraging the Cheeger inequality, we propose the simplicial spectral clustering algorithm. We report results from numerical experiments on synthetic and real-world network data to demonstrate the efficacy of the proposed approach.

cs.LG↗

arXiv2022

A Simple Way to Learn Metrics Between Attributed Graphs

The choice of good distances and similarity measures between objects is important for many machine learning methods. Therefore, many metric learning algorithms have been developed in recent years, mainly for Euclidean data in order to improve performance of classification or clustering methods. However, due to difficulties in establishing computable, efficient and differentiable distances between attributed graphs, few metric learning algorithms adapted to graphs have been developed despite the strong interest of the community. In this paper, we address this issue by proposing a new Simple Graph Metric Learning - SGML - model with few trainable parameters based on Simple Graph Convolutional Neural Networks - SGCN - and elements of Optimal Transport theory. This model allows us to build an appropriate distance from a database of labeled (attributed) graphs to improve the performance of simple classification algorithms such as $k$-NN. This distance can be quickly trained while maintaining good performances as illustrated by the experimental study presented in this paper.

cs.LG↗

arXiv2022

Probabilistic forecasts of extreme heatwaves using convolutional neural networks in a regime of lack of data

Understanding extreme events and their probability is key for the study of climate change impacts, risk assessment, adaptation, and the protection of living beings. Forecasting the occurrence probability of extreme heatwaves is a primary challenge for risk assessment and attribution, but also for fundamental studies about processes, dataset and model validation, and climate change studies. In this work we develop a methodology to build forecasting models which are based on convolutional neural networks, trained on extremely long climate model outputs. We demonstrate that neural networks have positive predictive skills, with respect to random climatological forecasts, for the occurrence of long-lasting 14-day heatwaves over France, up to 15 days ahead of time for fast dynamical drivers (500 hPa geopotential height fields), and also at much longer lead times for slow physical drivers (soil moisture). This forecast is made seamlessly in time and space, for fast hemispheric and slow local drivers. We find that the neural network selects extreme heatwaves associated with a North-Hemisphere wavenumber-3 pattern. The main scientific message is that most of the time, training neural networks for predicting extreme heatwaves occurs in a regime of lack of data. We suggest that this is likely to be the case for most other applications to large scale atmosphere and climate phenomena. For instance, using one hundred years-long training sets, a regime of drastic lack of data, leads to severely lower predictive skills and general inability to extract useful information available in the 500 hPa geopotential height field at a hemispheric scale in contrast to the dataset of several thousand years long. We discuss perspectives for dealing with the lack of data regime, for instance rare event simulations and how transfer learning may play a role in this latter task.

physics.ao-ph↗

arXiv2021

Fast Multiscale Diffusion on Graphs

Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the exponential, hence significantly improving a priori estimates of the polynomial order for a prescribed error. We further exploit properties of these approximations to factorize the computation of the action of the diffusion operator over multiple scales, thus reducing drastically its computational cost.

eess.SP↗

arXiv2021

Deep Learning-based Extreme Heatwave Forecast

Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics driven weather forecast systems or climate models can be used to forecast their occurrence or predict their probability. The present work explores the use of deep learning architectures, trained using outputs of a climate model, as an alternative strategy to forecast the occurrence of extreme long-lasting heatwaves. This new approach will be useful for several key scientific goals which include the study of climate model statistics, building a quantitative proxy for resampling rare events in climate models, study the impact of climate change, and should eventually be useful for forecasting. Fulfilling these important goals implies addressing issues such as class-size imbalance that is intrinsically associated with rare event prediction, assessing the potential benefits of transfer learning to address the nested nature of extreme events (naturally included in less extreme ones). We train a Convolutional Neural Network, using 1000 years of climate model outputs, with large-class undersampling and transfer learning. From the observed snapshots of the surface temperature and the 500 hPa geopotential height fields, the trained network achieves significant performance in forecasting the occurrence of long-lasting extreme heatwaves. We are able to predict them at three different levels of intensity, and as early as 15 days ahead of the start of the event (30 days ahead of the end of the event).

cs.LG↗

arXiv2020

Multiview Variational Graph Autoencoders for Canonical Correlation Analysis

We present a novel multiview canonical correlation analysis model based on a variational approach. This is the first nonlinear model that takes into account the available graph-based geometric constraints while being scalable for processing large scale datasets with multiple views. It is based on an autoencoder architecture with graph convolutional neural network layers. We experiment with our approach on classification, clustering, and recommendation tasks on real datasets. The algorithm is competitive with state-of-the-art multiview representation learning techniques.

cs.LG↗

arXiv2020

Hierarchical and Unsupervised Graph Representation Learning with Loukas's Coarsening

We propose a novel algorithm for unsupervised graph representation learning with attributed graphs. It combines three advantages addressing some current limitations of the literature: i) The model is inductive: it can embed new graphs without re-training in the presence of new data; ii) The method takes into account both micro-structures and macro-structures by looking at the attributed graphs at different scales; iii) The model is end-to-end differentiable: it is a building block that can be plugged into deep learning pipelines and allows for back-propagation. We show that combining a coarsening method having strong theoretical guarantees with mutual information maximization suffices to produce high quality embeddings. We evaluate them on classification tasks with common benchmarks of the literature. We show that our algorithm is competitive with state of the art among unsupervised graph representation learning methods.

cs.LG↗

arXiv2020

Asymptotic control of FWER under Gaussian assumption: application to correlation tests

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a unified framework to prove their asymptotic behavior which is valid in the case of highly correlated tests. We focus on correlation tests where several test statistics are proposed. All these multiple testing procedures on correlations are shown to control FWER. An extensive simulation study on correlation-based graph estimation highlights finite sample behavior, independence on the sparsity of graphs and dependence on the values of correlations. Empirical evaluation of power provides comparisons of the proposed methods. Finally validation of our procedures is proposed on real dataset of rats brain connectivity measured by fMRI. We confirm our theoretical findings by applying our procedures on a full null hypotheses with data from dead rats. Data on alive rats show the performance of the proposed procedures to correctly identify brain connectivity graphs with controlled errors.

math.ST↗

arXiv2019

Solving NMF with smoothness and sparsity constraints using PALM

Non-negative matrix factorization is a problem of dimensionality reduction and source separation of data that has been widely used in many fields since it was studied in depth in 1999 by Lee and Seung, including in compression of data, document clustering, processing of audio spectrograms and astronomy. In this work we have adapted a minimization scheme for convex functions with non-differentiable constraints called PALM to solve the NMF problem with solutions that can be smooth and/or sparse, two properties frequently desired.

cs.LG↗

arXiv2019

Combining traffic counts and Bluetooth data for link-origin-destination matrix estimation in large urban networks: The Brisbane case study

Origin-Destination matrix estimation is a keystone for traffic representation and analysis. Traditionally estimated thanks to traffic counts, surveys and socio-economic models, recent technological advances permit to rethink the estimation problem. Road user identification technologies, such as connected GPS, Bluetooth or Wifi detectors bring additional information, that is, for a fraction of the users, the origin, the destination and to some extend the itinerary taken. In the present work, this additional information is used for the estimation of a more comprehensive traffic representation tool: the link-origin-destination matrix. Such three-dimensional matrices extend the concept of traditional origin-destination matrices by also giving information on the traffic assignment. Their estimation is solved as an inverse problem whose objective function represents a trade-off between important properties the traffic has to satisfy. This article presents the theory and how to implement such method on real dataset. With the case study of Brisbane City where over 600 hundreds Bluetooth detectors have been installed it also illustrates the opportunities such link-origin-destination matrices create for traffic analysis.

eess.SP↗

arXiv2019

Graph-based era segmentation of international financial integration

Assessing world-wide financial integration constitutes a recurrent challenge in macroeconometrics, often addressed by visual inspections searching for data patterns. Econophysics literature enables us to build complementary, data-driven measures of financial integration using graphs. The present contribution investigates the potential and interests of a novel 3-step approach that combines several state-of-the-art procedures to i) compute graph-based representations of the multivariate dependence structure of asset prices time series representing the financial states of 32 countries world-wide (1955-2015); ii) compute time series of 5 graph-based indices that characterize the time evolution of the topologies of the graph; iii) segment these time evolutions in piece-wise constant eras, using an optimization framework constructed on a multivariate multi-norm total variation penalized functional. The method shows first that it is possible to find endogenous stable eras of world-wide financial integration. Then, our results suggest that the most relevant globalization eras would be based on the historical patterns of global capital flows, while the major regulatory events of the 1970s would only appear as a cause of sub-segmentation.

q-fin.GN↗