Non-negative matrix factorization is a problem of dimensionality reduction and source separation ... more 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.
2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI), 2021
The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-W... more The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-Wasserstein distances which resort to the Optimal Transport theory for comparing attributed graphs. In this paper, we address the open problem of optimizing the diffusion time used in these distances and which plays a key role in several machine learning settings, including graph domain adaptation or graph classification. Inspired from the notion of triplet-based constraints used, e.g., in metric learning, we design a loss function that aims at bringing two graphs closer together while keeping an impostor away, this latter taking the form of a Wasserstein barycenter. After a thorough analysis of the properties of this function, we show on synthetic and real-world data that the resulting Diffusion-Wasserstein distances outperforms the Gromov and Fused-Gromov Wasserstein distances on unsupervised graph domain adaptation tasks. Additionally, we give evidence in such a setting that our method for optimizing the diffusion parameter allows to overcome the limitation of the widely used circular validation strategy.
Null models have many applications on networks, from testing the significance of observations to ... more Null models have many applications on networks, from testing the significance of observations to the conception of algorithms such as community detection. They ususally preserve some network properties, such as degree distribution. Recently, some null-models have been proposed for spatial networks, and applied to the community detection problem. In this article, we propose a new null-model adapted to spatial networks, that, unlike previous ones, preserves both the spatial structure and the degrees of nodes. We show the efficacy of this null-model in the community detection case both on synthetic and collected networks.
Author manuscript, published in "N/A: [ ({date_debut_conf})]" Tracking of a dynamic gra... more Author manuscript, published in "N/A: [ ({date_debut_conf})]" Tracking of a dynamic graph using a signal theory approach:
Community shared bicycle systems, such as the Vélo’v program launched in Lyon in May 2005, are pu... more Community shared bicycle systems, such as the Vélo’v program launched in Lyon in May 2005, are public transportation programs that can be studied as a complex system composed of interconnected stations that exchange bicycles. They generate digital footprints that reveal the activity in the city over time and space, making possible a quantitative analysis of movements using bicycles in the city. A careful study relying on nonstationary statistical modeling and data mining allows us to first model the time evolution of the dynamics of movements with Vélo’v, that is mostly cyclostationary over the week with nonstationary evolutions over larger time-scales, and second to disentangle the spatial patterns to understand and visualize the flows of Vélo’v bicycles in the city. This study gives insights on the social behaviors of the users of this intermodal transportation system, the objective being to help in designing and planning policy in urban transportation.
We propose a novel algorithm for unsupervised graph representation learning with attributed graph... more 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.
Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to s... more Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of the brain activity. However, these analyses rapidly become complex and time-consuming. In this work, we present complementary empirical results on two tensor decomposition previously proposed named modified High Order Orthogonal Iteration (mHOOI) and High Order sparse Singular Value Decomposition (HOsSVD). These decompositions associated to k-means were shown to be useful for the study of multi trial functional connectivity dataset.
k-means est un algorithme celebre pour le clustering de donnees, mais ses performances se degrade... more k-means est un algorithme celebre pour le clustering de donnees, mais ses performances se degradent sur des donnees de grandes dimensions. Nous proposons des decompositions tensorielles parcimonieuses pour reduire la dimension des donnees avant d'appliquer k-means. Nous illustrons notre methode sur des mesures de connectivite fonctionnelle d'EEG de crises epileptiques. Abstract-k-means is famous to cluster a dataset, however it is known to perform badly on high dimensional data. To apply it on EEG functional connectivity measures, as function of the time and for different seizures of a same patient, we develop a new sparse tensorial decomposition to reduce the dimensions of the data before applying k-means.
Turbulence deals with the complex motions in fluid at high velocity and/or involving a large rang... more Turbulence deals with the complex motions in fluid at high velocity and/or involving a large range of length-scales. Turbulence asks then many questions from modeling this complexity to measuring it. In a first part, the description of signals measured in fluid turbulence experiments will be made along with a survey of modern signal processing tools that are adapted to their properties of scaling laws, multifractalty and non-stationarity. A second part will be devoted to the study of one signal processing framework, the decomposition of self-similar signals on the Mellin oscillating functions, that is a new way to probe jointly scale invariance and local organization of a signal. 1 Turbulence: experimental signals and signal processing tools 1.1 Preliminary analysis of fluid turbulence Formalization of the problem. Turbulence is first a problem of fluid mechanics [Bat67]. Let u(r(0); t) be the Lagrangian velocity of a fluid element that is in r(0) at initial time; ρ is its density. ...
Cet article porte sur le probleme d'adaptation de domaines par transport optimal entre deux g... more Cet article porte sur le probleme d'adaptation de domaines par transport optimal entre deux graphes. La tâche visee est le transfert de connaissance d'un graphe sourceetiquete pour aider la classification de noeuds d'un graphe cible nonetiquete. On s'interessea des scenarios ou se combinent une structure de graphe et des attributs associesa chaque noeud. L'approche proposee visea optimiser un mapping entre les deux graphes sous contraintes (i) de preservation des structures transportees et (ii) d'homogeneite desetiquettes transferees sur un meme noeud. Abstract-This paper addresses the problem of domain adaptation between two graphs by optimal transport. We aim at benefiting from the knowledge of a labeled source graph to improve the classification of nodes in an unlabeled target graph. We focus on the setting where a set of features is associated to each node of the graphs. The method presented in this paper optimizes a transportation plan from the source to...
Nous etudions le systeme Velo'v, un systeme automatise de location de velos a Lyon, en le rep... more Nous etudions le systeme Velo'v, un systeme automatise de location de velos a Lyon, en le representant sous la forme d'un reseau temporel. Une decomposition de ce reseau est proposee en utilisant une factorisation en matrices non-negatives (NMF), dont le choix des para-metres est discute. Cette decomposition permet de representer a chaque instant le reseau comme un melange de sous-reseaux, dont les structures decrivent des comportements specifiques des utilisateurs Velo'v, en lien avec l'espace geographique et socio-economique. Les coefficients d'activation associes a chacun des motifs permettent de separer temporellement ceux-ci, permettant une interpretation coherente avec la litterature sur les velos en libre-service.
Ce travail trouve son origine dans les études de l’auto-similarité par des déformation stationnar... more Ce travail trouve son origine dans les études de l’auto-similarité par des déformation stationnarisantes et porte sur des extensions aux champs bidimensionnels. Les symétries de champs 2D, images ou représentations à 2 paramètres d’un signal, sont envisagées, en particulier celle liées à l’invariance d’échelle. Nous donnons des résultats préliminaires portant sur les déformations stationnarisantes à deux dimensions, les modèles que l’on peut en déduire et montrons quelques exemples numériques portant sur la synthèse de tels champs, et l’analyse des déformations.
Bike sharing systems (BSS) have been growing fast all over the world, along with the number of ar... more Bike sharing systems (BSS) have been growing fast all over the world, along with the number of articles analyzing such systems. However the lack of databases at the individual level and covering several years has limited the analysis of BSS users' behavior in the long term. This article gives a first detailed description of the temporal evolution of individual customers. Using a 5-year dataset covering 120,827 distinct year-long subscribers, we show the heterogeneous individual trajectories masked by the overall system stability. Users follow two main trajectories: about half remain in the system for at most one year, showing a low median activity (47 trips); the remaining half corresponds to more active users (median activity of 91 trips in their first year) that remain continuously active for several years (mean time = 2.9 years). We show that users from urban cores, middle-aged and male are over represented among these long-term users, which profit most from the BSS. This provides further support for the view that BSS mostly benefit the already privileged.
The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is ... more The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is the Fourier Transform. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many scientific domains. With the explosion of digital data, both in quantity and diversity, the generalization of the tools based on Fourier Transform is mandatory. In data science, new problems arose for the processing of irregular data such as social networks, biological networks or other data on networks. Graph Signal Processing is a promising approach to deal with those. The present text is an overview of the state-of-the-art in Graph Signal Processing, focusing on how to define a Fourier Transform for data on graphs, how to interpret it and how to use it to process such data. It closes showing some examples of use. Along the way, the review reveals how Fourier's work remains modern and universal, and how his concepts, coming from physics and blended with mathematics, computer science and signal processing, play a key role to answer the modern challenges in data science.
In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic... more In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this seminal contribution, over the years, many studies have investigated the existence and form of scaling in Internet traffic. This contribution aims first at presenting a methodology, combining multiscale analysis (wavelet and wavelet leaders) and random projections (or sketches), permitting a precise, efficient and robust characterization of scaling which is capable of seeing through non-stationary anomalies. Second, we apply the methodology to a data set spanning an unusually long period: 14 years, from the MAWI traffic archive, thereby allowing an in-depth longitudinal analysis of the form, nature and evolutions of scaling in Internet traffic, as well as network mechanisms producing them. We also study a separate 3-day long trace to obtain complementary insight into intra-day behavior. We find that a biscaling (two ranges of independent scaling phenomena) regime is systematically observed: long-range dependence over the large scales, and multifractal-like scaling over the fine scales. We quantify the actual scaling ranges precisely, verify to high accuracy the expected relationship between the long range dependent parameter and the heavy tail parameter of the flow size distribution, and relate fine scale multifractal scaling to typical IP packet inter-arrival and to round-trip time distributions.
Structural interaction frequency matrices between all genome loci are now experimentally achievab... more Structural interaction frequency matrices between all genome loci are now experimentally achievable thanks to high-throughput chromosome conformation capture technologies. This ensues a new methodological challenge for computational biology which consists in objectively extracting from these data the structural motifs characteristic of genome organisation. We deployed the fast multi-scale community mining algorithm based on spectral graph wavelets to characterise the networks of intra-chromosomal interactions in human cell lines. We observed that there exist structural domains of all sizes up to chromosome length and demonstrated that the set of structural communities forms a hierarchy of chromosome segments. Hence, at all scales, chromosome folding predominantly involves interactions between neighbouring sites rather than the formation of links between distant loci. Multi-scale structural decomposition of human chromosomes provides an original framework to question structural organ...
2015 49th Asilomar Conference on Signals, Systems and Computers, 2015
Joint filtering of signals indexed on a graph consists in filtering not only the signal, but also... more Joint filtering of signals indexed on a graph consists in filtering not only the signal, but also the graph by an appropriate downsampling. Existing methods for filtering and downsampling graph signals approximate graphs as sums of bipartite graphs or use nodal domains of the Laplacian. Here, a different method is introduced, and is based on the partitioning in meaningful subgraphs of the graph itself, e.g. network's communities; this partition may be interpreted as a coarsening of the graph and may also be tailored to be aware of the signal structure. A method is proposed to create filterbanks that compute, for graph signals, an approximation and several details using the partition to downsample the graph. This means that we jointly filter the graph and the graph signal; it leads to the design of a new subgraphbased filterbank for graph signals. This design is tested on simple examples for compression and denoising.
2015 49th Asilomar Conference on Signals, Systems and Computers, 2015
Communities are an important type of structure in networks. Graph filters, such as wavelet filter... more Communities are an important type of structure in networks. Graph filters, such as wavelet filterbanks, have been used to detect such communities as groups of nodes more densely connected together than with the outsiders. When dealing with times series, it is possible to build a relational network based on the correlation matrix. However, in such a network, weights assigned to each edge have different properties than those of usual adjacency matrices. As a result, classical community detection methods based on modularity optimization are not consistent and the modularity needs to be redefined to take into account the structure of the correlation from random matrix theory. Here, we address how to detect communities from correlation matrices, by filtering global modes and random parts using properties that are specific to the distribution of correlation eigenvalues. Based on a Louvain approach, an algorithm to detect multiscale communities is also developed, which yields a weighted hierarchy of communities. The implementation of the method using graph filters is also discussed.
Art scholarship meets image processing algorithms ] Multiscale Anisotropic Texture Analysis and C... more Art scholarship meets image processing algorithms ] Multiscale Anisotropic Texture Analysis and Classification of Photographic Prints using spectral clustering, followed by a Ward linkage procedure. For proof of concept, these procedures are first applied to a reference data set of historic photographic papers that combine several levels of similarity and second to a large data set of culturally valuable photographic prints held by the Museum of Modern Art in New York. The characterization and clustering results are interpreted in collaboration with art scholars with an aim toward developing new modes of art historical research and humanities-based collaboration.
Non-negative matrix factorization is a problem of dimensionality reduction and source separation ... more 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.
2021 IEEE 33rd International Conference on Tools with Artificial Intelligence (ICTAI), 2021
The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-W... more The use of the heat kernel on graphs has recently given rise to a family of so-called Diffusion-Wasserstein distances which resort to the Optimal Transport theory for comparing attributed graphs. In this paper, we address the open problem of optimizing the diffusion time used in these distances and which plays a key role in several machine learning settings, including graph domain adaptation or graph classification. Inspired from the notion of triplet-based constraints used, e.g., in metric learning, we design a loss function that aims at bringing two graphs closer together while keeping an impostor away, this latter taking the form of a Wasserstein barycenter. After a thorough analysis of the properties of this function, we show on synthetic and real-world data that the resulting Diffusion-Wasserstein distances outperforms the Gromov and Fused-Gromov Wasserstein distances on unsupervised graph domain adaptation tasks. Additionally, we give evidence in such a setting that our method for optimizing the diffusion parameter allows to overcome the limitation of the widely used circular validation strategy.
Null models have many applications on networks, from testing the significance of observations to ... more Null models have many applications on networks, from testing the significance of observations to the conception of algorithms such as community detection. They ususally preserve some network properties, such as degree distribution. Recently, some null-models have been proposed for spatial networks, and applied to the community detection problem. In this article, we propose a new null-model adapted to spatial networks, that, unlike previous ones, preserves both the spatial structure and the degrees of nodes. We show the efficacy of this null-model in the community detection case both on synthetic and collected networks.
Author manuscript, published in "N/A: [ ({date_debut_conf})]" Tracking of a dynamic gra... more Author manuscript, published in "N/A: [ ({date_debut_conf})]" Tracking of a dynamic graph using a signal theory approach:
Community shared bicycle systems, such as the Vélo’v program launched in Lyon in May 2005, are pu... more Community shared bicycle systems, such as the Vélo’v program launched in Lyon in May 2005, are public transportation programs that can be studied as a complex system composed of interconnected stations that exchange bicycles. They generate digital footprints that reveal the activity in the city over time and space, making possible a quantitative analysis of movements using bicycles in the city. A careful study relying on nonstationary statistical modeling and data mining allows us to first model the time evolution of the dynamics of movements with Vélo’v, that is mostly cyclostationary over the week with nonstationary evolutions over larger time-scales, and second to disentangle the spatial patterns to understand and visualize the flows of Vélo’v bicycles in the city. This study gives insights on the social behaviors of the users of this intermodal transportation system, the objective being to help in designing and planning policy in urban transportation.
We propose a novel algorithm for unsupervised graph representation learning with attributed graph... more 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.
Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to s... more Functional connectivity (FC) is a graph-like data structure commonly used by neuroscientists to study the dynamic behaviour of the brain activity. However, these analyses rapidly become complex and time-consuming. In this work, we present complementary empirical results on two tensor decomposition previously proposed named modified High Order Orthogonal Iteration (mHOOI) and High Order sparse Singular Value Decomposition (HOsSVD). These decompositions associated to k-means were shown to be useful for the study of multi trial functional connectivity dataset.
k-means est un algorithme celebre pour le clustering de donnees, mais ses performances se degrade... more k-means est un algorithme celebre pour le clustering de donnees, mais ses performances se degradent sur des donnees de grandes dimensions. Nous proposons des decompositions tensorielles parcimonieuses pour reduire la dimension des donnees avant d'appliquer k-means. Nous illustrons notre methode sur des mesures de connectivite fonctionnelle d'EEG de crises epileptiques. Abstract-k-means is famous to cluster a dataset, however it is known to perform badly on high dimensional data. To apply it on EEG functional connectivity measures, as function of the time and for different seizures of a same patient, we develop a new sparse tensorial decomposition to reduce the dimensions of the data before applying k-means.
Turbulence deals with the complex motions in fluid at high velocity and/or involving a large rang... more Turbulence deals with the complex motions in fluid at high velocity and/or involving a large range of length-scales. Turbulence asks then many questions from modeling this complexity to measuring it. In a first part, the description of signals measured in fluid turbulence experiments will be made along with a survey of modern signal processing tools that are adapted to their properties of scaling laws, multifractalty and non-stationarity. A second part will be devoted to the study of one signal processing framework, the decomposition of self-similar signals on the Mellin oscillating functions, that is a new way to probe jointly scale invariance and local organization of a signal. 1 Turbulence: experimental signals and signal processing tools 1.1 Preliminary analysis of fluid turbulence Formalization of the problem. Turbulence is first a problem of fluid mechanics [Bat67]. Let u(r(0); t) be the Lagrangian velocity of a fluid element that is in r(0) at initial time; ρ is its density. ...
Cet article porte sur le probleme d'adaptation de domaines par transport optimal entre deux g... more Cet article porte sur le probleme d'adaptation de domaines par transport optimal entre deux graphes. La tâche visee est le transfert de connaissance d'un graphe sourceetiquete pour aider la classification de noeuds d'un graphe cible nonetiquete. On s'interessea des scenarios ou se combinent une structure de graphe et des attributs associesa chaque noeud. L'approche proposee visea optimiser un mapping entre les deux graphes sous contraintes (i) de preservation des structures transportees et (ii) d'homogeneite desetiquettes transferees sur un meme noeud. Abstract-This paper addresses the problem of domain adaptation between two graphs by optimal transport. We aim at benefiting from the knowledge of a labeled source graph to improve the classification of nodes in an unlabeled target graph. We focus on the setting where a set of features is associated to each node of the graphs. The method presented in this paper optimizes a transportation plan from the source to...
Nous etudions le systeme Velo'v, un systeme automatise de location de velos a Lyon, en le rep... more Nous etudions le systeme Velo'v, un systeme automatise de location de velos a Lyon, en le representant sous la forme d'un reseau temporel. Une decomposition de ce reseau est proposee en utilisant une factorisation en matrices non-negatives (NMF), dont le choix des para-metres est discute. Cette decomposition permet de representer a chaque instant le reseau comme un melange de sous-reseaux, dont les structures decrivent des comportements specifiques des utilisateurs Velo'v, en lien avec l'espace geographique et socio-economique. Les coefficients d'activation associes a chacun des motifs permettent de separer temporellement ceux-ci, permettant une interpretation coherente avec la litterature sur les velos en libre-service.
Ce travail trouve son origine dans les études de l’auto-similarité par des déformation stationnar... more Ce travail trouve son origine dans les études de l’auto-similarité par des déformation stationnarisantes et porte sur des extensions aux champs bidimensionnels. Les symétries de champs 2D, images ou représentations à 2 paramètres d’un signal, sont envisagées, en particulier celle liées à l’invariance d’échelle. Nous donnons des résultats préliminaires portant sur les déformations stationnarisantes à deux dimensions, les modèles que l’on peut en déduire et montrons quelques exemples numériques portant sur la synthèse de tels champs, et l’analyse des déformations.
Bike sharing systems (BSS) have been growing fast all over the world, along with the number of ar... more Bike sharing systems (BSS) have been growing fast all over the world, along with the number of articles analyzing such systems. However the lack of databases at the individual level and covering several years has limited the analysis of BSS users' behavior in the long term. This article gives a first detailed description of the temporal evolution of individual customers. Using a 5-year dataset covering 120,827 distinct year-long subscribers, we show the heterogeneous individual trajectories masked by the overall system stability. Users follow two main trajectories: about half remain in the system for at most one year, showing a low median activity (47 trips); the remaining half corresponds to more active users (median activity of 91 trips in their first year) that remain continuously active for several years (mean time = 2.9 years). We show that users from urban cores, middle-aged and male are over represented among these long-term users, which profit most from the BSS. This provides further support for the view that BSS mostly benefit the already privileged.
The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is ... more The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that is the Fourier Transform. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many scientific domains. With the explosion of digital data, both in quantity and diversity, the generalization of the tools based on Fourier Transform is mandatory. In data science, new problems arose for the processing of irregular data such as social networks, biological networks or other data on networks. Graph Signal Processing is a promising approach to deal with those. The present text is an overview of the state-of-the-art in Graph Signal Processing, focusing on how to define a Fourier Transform for data on graphs, how to interpret it and how to use it to process such data. It closes showing some examples of use. Along the way, the review reveals how Fourier's work remains modern and universal, and how his concepts, coming from physics and blended with mathematics, computer science and signal processing, play a key role to answer the modern challenges in data science.
In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic... more In the mid-90's, it was shown that the statistics of aggregated time series from Internet traffic departed from those of traditional short range dependent models, and were instead characterized by asymptotic self-similarity. Following this seminal contribution, over the years, many studies have investigated the existence and form of scaling in Internet traffic. This contribution aims first at presenting a methodology, combining multiscale analysis (wavelet and wavelet leaders) and random projections (or sketches), permitting a precise, efficient and robust characterization of scaling which is capable of seeing through non-stationary anomalies. Second, we apply the methodology to a data set spanning an unusually long period: 14 years, from the MAWI traffic archive, thereby allowing an in-depth longitudinal analysis of the form, nature and evolutions of scaling in Internet traffic, as well as network mechanisms producing them. We also study a separate 3-day long trace to obtain complementary insight into intra-day behavior. We find that a biscaling (two ranges of independent scaling phenomena) regime is systematically observed: long-range dependence over the large scales, and multifractal-like scaling over the fine scales. We quantify the actual scaling ranges precisely, verify to high accuracy the expected relationship between the long range dependent parameter and the heavy tail parameter of the flow size distribution, and relate fine scale multifractal scaling to typical IP packet inter-arrival and to round-trip time distributions.
Structural interaction frequency matrices between all genome loci are now experimentally achievab... more Structural interaction frequency matrices between all genome loci are now experimentally achievable thanks to high-throughput chromosome conformation capture technologies. This ensues a new methodological challenge for computational biology which consists in objectively extracting from these data the structural motifs characteristic of genome organisation. We deployed the fast multi-scale community mining algorithm based on spectral graph wavelets to characterise the networks of intra-chromosomal interactions in human cell lines. We observed that there exist structural domains of all sizes up to chromosome length and demonstrated that the set of structural communities forms a hierarchy of chromosome segments. Hence, at all scales, chromosome folding predominantly involves interactions between neighbouring sites rather than the formation of links between distant loci. Multi-scale structural decomposition of human chromosomes provides an original framework to question structural organ...
2015 49th Asilomar Conference on Signals, Systems and Computers, 2015
Joint filtering of signals indexed on a graph consists in filtering not only the signal, but also... more Joint filtering of signals indexed on a graph consists in filtering not only the signal, but also the graph by an appropriate downsampling. Existing methods for filtering and downsampling graph signals approximate graphs as sums of bipartite graphs or use nodal domains of the Laplacian. Here, a different method is introduced, and is based on the partitioning in meaningful subgraphs of the graph itself, e.g. network's communities; this partition may be interpreted as a coarsening of the graph and may also be tailored to be aware of the signal structure. A method is proposed to create filterbanks that compute, for graph signals, an approximation and several details using the partition to downsample the graph. This means that we jointly filter the graph and the graph signal; it leads to the design of a new subgraphbased filterbank for graph signals. This design is tested on simple examples for compression and denoising.
2015 49th Asilomar Conference on Signals, Systems and Computers, 2015
Communities are an important type of structure in networks. Graph filters, such as wavelet filter... more Communities are an important type of structure in networks. Graph filters, such as wavelet filterbanks, have been used to detect such communities as groups of nodes more densely connected together than with the outsiders. When dealing with times series, it is possible to build a relational network based on the correlation matrix. However, in such a network, weights assigned to each edge have different properties than those of usual adjacency matrices. As a result, classical community detection methods based on modularity optimization are not consistent and the modularity needs to be redefined to take into account the structure of the correlation from random matrix theory. Here, we address how to detect communities from correlation matrices, by filtering global modes and random parts using properties that are specific to the distribution of correlation eigenvalues. Based on a Louvain approach, an algorithm to detect multiscale communities is also developed, which yields a weighted hierarchy of communities. The implementation of the method using graph filters is also discussed.
Art scholarship meets image processing algorithms ] Multiscale Anisotropic Texture Analysis and C... more Art scholarship meets image processing algorithms ] Multiscale Anisotropic Texture Analysis and Classification of Photographic Prints using spectral clustering, followed by a Ward linkage procedure. For proof of concept, these procedures are first applied to a reference data set of historic photographic papers that combine several levels of similarity and second to a large data set of culturally valuable photographic prints held by the Museum of Modern Art in New York. The characterization and clustering results are interpreted in collaboration with art scholars with an aim toward developing new modes of art historical research and humanities-based collaboration.
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Papers by Pierre Borgnat