Tesis sobre el tema "Statistiques géométriques"
Crea una cita precisa en los estilos APA, MLA, Chicago, Harvard y otros
Consulte los 47 mejores tesis para su investigación sobre el tema "Statistiques géométriques".
Junto a cada fuente en la lista de referencias hay un botón "Agregar a la bibliografía". Pulsa este botón, y generaremos automáticamente la referencia bibliográfica para la obra elegida en el estilo de cita que necesites: APA, MLA, Harvard, Vancouver, Chicago, etc.
También puede descargar el texto completo de la publicación académica en formato pdf y leer en línea su resumen siempre que esté disponible en los metadatos.
Explore tesis sobre una amplia variedad de disciplinas y organice su bibliografía correctamente.
Miolane, Nina. "Statistiques géométriques pour l'anatomie numérique". Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4146/document.
This thesis develops Geometric Statistics to analyze the normal andpathological variability of organ shapes in Computational Anatomy. Geometricstatistics consider data that belong to manifolds with additional geometricstructures. In Computational Anatomy, organ shapes may be modeled asdeformations of a template - i.e. as elements of a Lie group, a manifold with agroup structure - or as the equivalence classes of their 3D configurations underthe action of transformations - i.e. as elements of a quotient space, a manifoldwith a stratification. Medical images can be modeled as manifolds with ahorizontal distribution. The contribution of this thesis is to extend GeometricStatistics beyond the now classical Riemannian and metric geometries in orderto account for these additional structures. First, we tackle the definition ofGeometric Statistics on Lie groups. We provide an algorithm that constructs a(pseudo-)Riemannian metric compatible with the group structure when itexists. We find that some groups do not admit such a (pseudo-)metric andadvocate for non-metric statistics on Lie groups. Second, we use GeometricStatistics to analyze the algorithm of organ template computation. We show itsasymptotic bias by considering the geometry of quotient spaces. We illustratethe bias on brain templates and suggest an improved algorithm. We then showthat registering organ shapes induces a bias in their statistical analysis, whichwe offer to correct. Third, we apply Geometric Statistics to medical imageprocessing, providing the mathematics to extend sub-Riemannian structures,already used in 2D, to our 3D images
Vauglin, François. "Modèles statistiques des imprécisions géométriques des objets géographiques linéaires". Université de Marne-la-Vallée, 1997. http://www.theses.fr/1997MARN0010.
Formont, Pierre. "Outils statistiques et géométriques pour la classification des images SAR polarimétriques hautement texturées". Phd thesis, Université Rennes 1, 2013. http://tel.archives-ouvertes.fr/tel-00983304.
Formont, P. "Outils statistiques et géométriques pour la classification des images SAR polarimétriques hautement texturées". Phd thesis, Supélec, 2013. http://tel.archives-ouvertes.fr/tel-01020050.
Ghorbel, Faouzi. "Vers une approche unifiée des aspects géométriques et statistiques de la reconnaissance de formes planes". Rennes 1, 1990. http://www.theses.fr/1990REN10131.
Krzakala, Florent. "Aspects géométriques et paysages d'énergies des verres de spins : étude d'un système désordonné et frustré en dimension finie". Paris 6, 2002. https://tel.archives-ouvertes.fr/tel-00002232.
Krzakala, Florent. "Aspects géométriques et paysage d'énergie des verres de spins: étude d'un système désordonné et frustré en dimension finie". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2002. http://tel.archives-ouvertes.fr/tel-00002232.
Bonis, Thomas. "Algorithmes d'apprentissage statistique pour l'analyse géométrique et topologique de données". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS459/document.
In this thesis, we study data analysis algorithms using random walks on neighborhood graphs, or random geometric graphs. It is known random walks on such graphs approximate continuous objects called diffusion processes. In the first part of this thesis, we use this approximation result to propose a new soft clustering algorithm based on the mode seeking framework. For our algorithm, we want to define clusters using the properties of a diffusion process. Since we do not have access to this continuous process, our algorithm uses a random walk on a random geometric graph instead. After proving the consistency of our algorithm, we evaluate its efficiency on both real and synthetic data. We then deal tackle the issue of the convergence of invariant measures of random walks on random geometric graphs. As these random walks converge to a diffusion process, we can expect their invariant measures to converge to the invariant measure of this diffusion process. Using an approach based on Stein's method, we manage to obtain quantitfy this convergence. Moreover, the method we use is more general and can be used to obtain other results such as convergence rates for the Central Limit Theorem. In the last part of this thesis, we use the concept of persistent homology, a concept of algebraic topology, to improve the pooling step of the bag-of-words approach for 3D shapes
Aamari, Eddie. "Vitesses de convergence en inférence géométrique". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS203.
Some datasets exhibit non-trivial geometric or topological features that can be interesting to infer.This thesis deals with non-asymptotic rates for various geometric quantities associated with submanifolds M ⊂ RD. In all the settings, we are given an i.i.d. n-sample with common distribution P having support M. We study the optimal rates of estimation of the submanifold M for the loss given by the Hausdorff metric, of the reach τM, of the tangent space TX M and the second fundamental form I I MX, for X ∈ M both deterministic and random.The rates are given in terms of the sample size n, the instrinsic dimension of M, and its smoothness.In the process, we obtain stability results for existing reconstruction techniques, a denoising procedure and results on the geometry of the reach τM. An extension of Assouad's lemma is presented, allowing to derive minimax lower bounds in singular frameworks
Flandin, Guillaume. "Utilisation d'informations géométriques pour l'analyse statistique des données d'IRM fonctionnelle". Phd thesis, Université de Nice Sophia-Antipolis, 2004. http://tel.archives-ouvertes.fr/tel-00633520.
Brécheteau, Claire. "Vers une vision robuste de l'inférence géométrique". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS334/document.
It is primordial to establish effective and robust methods to extract pertinent information from datasets. We focus on datasets that can be represented as point clouds in some metric space, e.g. Euclidean space R^d; and that are generated according to some distribution. Of the natural questions that may arise when one has access to data, three are addressed in this thesis. The first question concerns the comparison of two sets of points. How to decide whether two datasets have been generated according to similar distributions? We build a statistical test allowing to one to decide whether two point clouds have been generated from distributions that are equal (up to some rigid transformation e.g. symmetry, translation, rotation...).The second question is about the decomposition of a set of points into clusters. Given a point cloud, how does one make relevant clusters? Often, it consists of selecting a set of k representatives, and associating every point to its closest representative (in some sense to be defined). We develop methods suited to data sampled according to some mixture of k distributions, possibly with outliers. Finally, when the data can not be grouped naturally into $k$ clusters, e.g. when they are generated in a close neighborhood of some sub-manifold in R^d, a more relevant question is the following. How to build a system of $k$ representatives, with k large, from which it is possible to recover the sub-manifold? This last question is related to the problems of quantization and compact set inference. To address it, we introduce and study a modification of the $k$-means method adapted to the presence of outliers, in the context of quantization. The answers we bring in this thesis are of two types, theoretical and algorithmic. The methods we develop are based on continuous objects built from distributions and sub-measures. Statistical studies allow us to measure the proximity between the empirical objects and the continuous ones. These methods are easy to implement in practice, when samples of points are available. The main tool in this thesis is the function distance-to-measure, which was originally introduced to make topological data analysis work in the presence of outliers
Xia, Gui-Song. "Méthodes géométriques pour l'analyse d'images et de textures". Paris, Télécom ParisTech, 2011. https://pastel.archives-ouvertes.fr/pastel-00682590.
This thesis focuses on the studies of the extraction and characterization of local image structures, in the context of images and texture analysis. Relying on the level lines of images or on the somehow dual and less structured notion of gradient orientation, the contributions of the thesis concentrate on following three themes: The first part of this thesis presents a new method for texture analysis that in spirit is similar to morphological granulometries, while allowing a high degree of geometrical and radiometric invariances. Also using the topographic map representation, the second part of this thesis develops a general approach for the abstraction of images, the aim of which is to automatically generate abstract images from realistic photographs. The subject of the last part of this thesis is the detection of junctions in natural images. The approach relies on the local directions of level lines through the orientation of image gradient. We introduce a generic junction analysis scheme. The first asset of the proposed procedure is an automatic criterion for the detection of junctions, permitting to deal with textured parts in which no detection is expected. Second, the method yields a characterization of L-, Y- and X- junctions, including a precise computation of their type, localization and scale. Contrary to classical approaches, scale characterization does not rely on the linear scale-space, therefore enabling geometric accuracy
Pedersen, Morten Akhøj. "Méthodes riemanniennes et sous-riemanniennes pour la réduction de dimension". Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4087.
In this thesis, we propose new methods for dimension reduction based on differential geometry, that is, finding a representation of a set of observations in a space of lower dimension than the original data space. Methods for dimension reduction form a cornerstone of statistics, and thus have a very wide range of applications. For instance, a lower dimensional representation of a data set allows visualization and is often necessary for subsequent statistical analyses. In ordinary Euclidean statistics, the data belong to a vector space and the lower dimensional space might be a linear subspace or a non-linear submanifold approximating the observations. The study of such smooth manifolds, differential geometry, naturally plays an important role in this last case, or when the data space is itself a known manifold. Methods for analysing this type of data form the field of geometric statistics. In this setting, the approximating space found by dimension reduction is naturally a submanifold of the given manifold. The starting point of this thesis is geometric statistics for observations belonging to a known Riemannian manifold, but parts of our work form a contribution even in the case of data belonging to Euclidean space, mathbb{R}^d.An important example of manifold valued data is shapes, in our case discrete or continuous curves or surfaces. In evolutionary biology, researchers are interested in studying reasons for and implications of morphological differences between species. Shape is one way to formalize morphology. This application motivates the first main contribution of the thesis. We generalize a dimension reduction method used in evolutionary biology, phylogenetic principal component analysis (P-PCA), to work for data on a Riemannian manifold - so that it can be applied to shape data. P-PCA is a version of PCA for observations that are assumed to be leaf nodes of a phylogenetic tree. From a statistical point of view, the important property of such data is that the observations (leaf node values) are not necessarily independent. We define and estimate intrinsic weighted means and covariances on a manifold which takes the dependency of the observations into account. We then define phylogenetic PCA on a manifold to be the eigendecomposition of the weighted covariance in the tangent space of the weighted mean. We show that the mean estimator that is currently used in evolutionary biology for studying morphology corresponds to taking only a single step of our Riemannian gradient descent algorithm for the intrinsic mean, when the observations are represented in Kendall's shape space. Our second main contribution is a non-parametric method for dimension reduction that can be used for approximating a set of observations based on a very flexible class of submanifolds. This method is novel even in the case of Euclidean data. The method works by constructing a subbundle of the tangent bundle on the data manifold via local PCA. We call this subbundle the principal subbundle. We then observe that this subbundle induces a sub-Riemannian structure and we show that the resulting sub-Riemannian geodesics with respect to this structure stay close to the set of observations. Moreover, we show that sub-Riemannian geodesics starting from a given point locally generate a submanifold which is radially aligned with the estimated subbundle, even for non-integrable subbundles. Non-integrability is likely to occur when the subbundle is estimated from noisy data, and our method demonstrates that sub-Riemannian geometry is a natural framework for dealing which such problems. Numerical experiments illustrate the power of our framework by showing that we can achieve impressively large range reconstructions even in the presence of quite high levels of noise
I denne afhandling præsenteres nye metoder til dimensionsreduktion, baseret p˚adifferential geometri. Det vil sige metoder til at finde en repræsentation af et datasæti et rum af lavere dimension end det opringelige rum. S˚adanne metoder spiller enhelt central rolle i statistik, og har et meget bredt anvendelsesomr˚ade. En laveredimensionalrepræsentation af et datasæt tillader visualisering og er ofte nødvendigtfor efterfølgende statistisk analyse. I traditionel, Euklidisk statistik ligger observationernei et vektor rum, og det lavere-dimensionale rum kan være et lineært underrumeller en ikke-lineær undermangfoldighed som approksimerer observationerne.Studiet af s˚adanne glatte mangfoldigheder, differential geometri, spiller en vigtig rollei sidstnævnte tilfælde, eller hvis rummet hvori observationerne ligger i sig selv er enmangfoldighed. Metoder til at analysere observationer p˚a en mangfoldighed udgørfeltet geometrisk statistik. I denne kontekst er det approksimerende rum, fundetvia dimensionsreduktion, naturligt en submangfoldighed af den givne mangfoldighed.Udgangspunktet for denne afhandling er geometrisk statistik for observationer p˚a ena priori kendt Riemannsk mangfoldighed, men dele af vores arbejde udgør et bidragselv i tilfældet med observationer i Euklidisk rum, Rd.Et vigtigt eksempel p˚a data p˚a en mangfoldighed er former, i vores tilfældediskrete kurver eller overflader. I evolutionsbiologi er forskere interesseret i at studeregrunde til og implikationer af morfologiske forskelle mellem arter. Former er ´en m˚adeat formalisere morfologi p˚a. Denne anvendelse motiverer det første hovedbidrag idenne afhandling. We generaliserer en metode til dimensionsreduktion brugt i evolutionsbiologi,phylogenetisk principal component analysis (P-PCA), til at virke for datap˚a en Riemannsk mangfoldighed - s˚a den kan anvendes til observationer af former. PPCAer en version af PCA for observationer som antages at være de yderste knuder iet phylogenetisk træ. Fra et statistisk synspunkt er den vigtige egenskab ved s˚adanneobservationer at de ikke nødvendigvis er uafhængige. We definerer og estimerer intrinsiskevægtede middelværdier og kovarianser p˚a en mangfoldighed, som tager højde fors˚adanne observationers afhængighed. Vi definerer derefter phylogenetisk PCA p˚a enmangfoldighed som egendekomposition af den vægtede kovarians i tanget-rummet tilden vægtede middelværdi. Vi viser at estimatoren af middelværdien som pt. bruges ievolutionsbiologi til at studere morfologi svarer til at tage kun et enkelt skridt af voresRiemannske gradient descent algoritme for den intrinsiske middelværdi, n˚ar formernerepræsenteres i Kendall´s form-mangfoldighed.Vores andet hovedbidrag er en ikke-parametrisk metode til dimensionsreduktionsom kan bruges til at approksimere et data sæt baseret p˚a en meget flexibel klasse afsubmangfoldigheder. Denne metode er ny ogs˚a i tilfældet med Euklidisk data. Metodenvirker ved at konstruere et under-bundt af tangentbundet p˚a datamangfoldighedenM via lokale PCA´er. Vi kalder dette underbundt principal underbundtet. Viobserverer at dette underbundt inducerer en sub-Riemannsk struktur p˚a M og vi viserat sub-Riemannske geodæter fra et givent punkt lokalt genererer en submangfoldighedsom radialt flugter med det estimerede subbundt, selv for ikke-integrable subbundter.Ved støjfyldt data forekommer ikke-integrabilitet med stor sandsynlighed, og voresmetode demonstrerer at sub-Riemannsk geometri er en naturlig tilgang til at h˚andteredette. Numeriske eksperimenter illustrerer styrkerne ved metoden ved at vise at denopn˚ar rekonstruktioner over store afstande, selv under høje niveauer af støj
Zhu, Zuowei. "Modèles géométriques avec defauts pour la fabrication additive". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLN021/document.
The intricate error sources within different stages of the Additive Manufacturing (AM) process have brought about major issues regarding the dimensional and geometrical accuracy of the manufactured product. Therefore, effective modeling of the geometric deviations is critical for AM. The Skin Model Shapes (SMS) paradigm offers a comprehensive framework aiming at addressing the deviation modeling problem at different stages of product lifecycle, and is thus a promising solution for deviation modeling in AM. In this thesis, considering the layer-wise characteristic of AM, a new SMS framework is proposed which characterizes the deviations in AM with in-plane and out-of-plane perspectives. The modeling of in-plane deviation aims at capturing the variability of the 2D shape of each layer. A shape transformation perspective is proposed which maps the variational effects of deviation sources into affine transformations of the nominal shape. With this assumption, a parametric deviation model is established based on the Polar Coordinate System which manages to capture deviation patterns regardless of the shape complexity. This model is further enhanced with a statistical learning capability to simultaneously learn from deviation data of multiple shapes and improve the performance on all shapes.Out-of-plane deviation is defined as the deformation of layer in the build direction. A layer-level investigation of out-of-plane deviation is conducted with a data-driven method. Based on the deviation data collected from a number of Finite Element simulations, two modal analysis methods, Discrete Cosine Transform (DCT) and Statistical Shape Analysis (SSA), are adopted to identify the most significant deviation modes in the layer-wise data. The effect of part and process parameters on the identified modes is further characterized with a Gaussian Process (GP) model. The discussed methods are finally used to obtain high-fidelity SMSs of AM products by deforming the nominal layer contours with predicted deviations and rebuilding the complete non-ideal surface model from the deformed contours. A toolbox is developed in the MATLAB environment to demonstrate the effectiveness of the proposed methods
Deveaux, Vincent. "Modèles markoviens partiellement orientés. Approche géométrique des Automates cellulaires probabilistes". Phd thesis, Université de Rouen, 2008. http://tel.archives-ouvertes.fr/tel-00325051.
Au cours de la première, nous définissons la notion de chaîne partiellement ordonnée qui généralise celle d'automate cellulaire probabiliste. Cette définition se fait par l'intermédiaire de spécification partiellement ordonnée de la même façon que les mesures de Gibbs sont définies à l'aide de spécifications. Nous obtenons des résultats analogues sur l'espace des phases : caractérisation des mesures extrêmes, construction/reconstruction en partant des noyaux sur un seul site, critères d'unicité. Les résultats sont appliqués tout au long du texte à des automates déjà connus.
La deuxième partie est essentiellement vouée à l'étude d'automates cellulaires unidimensionnels à deux voisins et deux états. Nous donnons deux décompositions des configurations spatio-temporelles en flot d'information. Ces flots ont une signification géométrique. De cela nous tirons deux critères d'unicité.
En annexe, nous donnons une démonstration de transition de phase d'un automate cellulaire défini par A. Toom, le modèle NEC. Tout au long du texte, des simulations sont présentées.
Castonguay, Jean-Philippe. "Contribution à la modélisation statistique du comportement énergétique et géométrique de la batterie LMP". Mémoire, École de technologie supérieure, 2007. http://espace.etsmtl.ca/1078/1/CASTONGUAY_Jean%2DPhilippe.pdf.
Matei, Cornel-Marius. "Comparaison entre les approches statistique et géométrique dans la détection des détection des défaillances". Lille 1, 2000. http://www.theses.fr/2000LIL10125.
Deveaux, Vincent. "Modèles markoviens partiellement orientés. Approche géométrique des automates cellulaires probabilistes". Phd thesis, Rouen, 2008. http://www.theses.fr/2008ROUES004.
The global subject of this thesis is probabilistic cellular automata (PCA). It is divided into two parts. In the first part, we define the notion of partially ordered chains (POC) that generalise PCA. They are defined thought partially ordered specification (POS) in analogy with the statistical mechanics notion of Gibbs measure. We obtain the analogous of Gibbs measure phase space properties characterization of extremal measures, construction/reconstruction starting from single site kernels, criterion of uniqueness. These results are applied to some well-known PCA. The second part is essentially devoted to 1-dimensional PCA with two neighbours and two states. We show two decompositions of space-time configurations in flow of information. Those flows have a geometrical meaning that induce two uniqueness criteria. In appendix, we give a version of the proof of phase transition of the NEC Toom's PCA. The whole thesis is punctuated by simulations
Lepoultier, Guilhem. "Transport numérique de quantités géométriques". Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112202/document.
In applied mathematics, question of moving quantities by vector is an important question : fluid mechanics, kinetic theory… Using particle methods, we're going to move an additional quantity giving more information on the problem. First part of the work is the theorical formulation for this kind of transport. It's going to use the differential in space of the vector field to compute the differential of the flow. An immediate and natural application is density who are parametrized by and point and a tensor, like gaussians. We're going to move such densities by moving point and tensor. Natural question is now the accuracy of such approximation. It's second part of our work , which discuss of distance to estimate such type of densities
Sidobre, Daniel. "Raisonnement géométrique et synthèse de stratégies d'assemblage en robotique". Toulouse 3, 1990. http://www.theses.fr/1990TOU30102.
Térouanne, Eric. "A propos de quelques modèles mathématiques". Montpellier 2, 1987. http://www.theses.fr/1987MON20266.
Maignant, Elodie. "Plongements barycentriques pour l'apprentissage géométrique de variétés : application aux formes et graphes". Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4096.
An MRI image has over 60,000 pixels. The largest known human protein consists of around 30,000 amino acids. We call such data high-dimensional. In practice, most high-dimensional data is high-dimensional only artificially. For example, of all the images that could be randomly generated by coloring 256 x 256 pixels, only a very small subset would resemble an MRI image of a human brain. This is known as the intrinsic dimension of such data. Therefore, learning high-dimensional data is often synonymous with dimensionality reduction. There are numerous methods for reducing the dimension of a dataset, the most recent of which can be classified according to two approaches.A first approach known as manifold learning or non-linear dimensionality reduction is based on the observation that some of the physical laws behind the data we observe are non-linear. In this case, trying to explain the intrinsic dimension of a dataset with a linear model is sometimes unrealistic. Instead, manifold learning methods assume a locally linear model.Moreover, with the emergence of statistical shape analysis, there has been a growing awareness that many types of data are naturally invariant to certain symmetries (rotations, reparametrizations, permutations...). Such properties are directly mirrored in the intrinsic dimension of such data. These invariances cannot be faithfully transcribed by Euclidean geometry. There is therefore a growing interest in modeling such data using finer structures such as Riemannian manifolds. A second recent approach to dimension reduction consists then in generalizing existing methods to non-Euclidean data. This is known as geometric learning.In order to combine both geometric learning and manifold learning, we investigated the method called locally linear embedding, which has the specificity of being based on the notion of barycenter, a notion a priori defined in Euclidean spaces but which generalizes to Riemannian manifolds. In fact, the method called barycentric subspace analysis, which is one of those generalizing principal component analysis to Riemannian manifolds, is based on this notion as well. Here we rephrase both methods under the new notion of barycentric embeddings. Essentially, barycentric embeddings inherit the structure of most linear and non-linear dimension reduction methods, but rely on a (locally) barycentric -- affine -- model rather than a linear one.The core of our work lies in the analysis of these methods, both on a theoretical and practical level. In particular, we address the application of barycentric embeddings to two important examples in geometric learning: shapes and graphs. In addition to practical implementation issues, each of these examples raises its own theoretical questions, mostly related to the geometry of quotient spaces. In particular, we highlight that compared to standard dimension reduction methods in graph analysis, barycentric embeddings stand out for their better interpretability. In parallel with these examples, we characterize the geometry of locally barycentric embeddings, which generalize the projection computed by locally linear embedding. Finally, algorithms for geometric manifold learning, novel in their approach, complete this work
Bertrand, Samuel. "Modélisation géométrique 3D in vivo du tronc humain à partir de l'imageur basse dose EOS". Phd thesis, Paris, ENSAM, 2005. http://pastel.archives-ouvertes.fr/pastel-00001505.
Godichon-Baggioni, Antoine. "Algorithmes stochastiques pour la statistique robuste en grande dimension". Thesis, Dijon, 2016. http://www.theses.fr/2016DIJOS053/document.
This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the mean and the covariance. We will focus on robust estimates, which are not too much sensitive to outliers.In a first part, we are interested in the recursive estimation of the geometric median, which is a robust indicator of location which can so be preferred to the mean when a part of the studied data is contaminated. For this purpose, we introduce a Robbins-Monro algorithm as well as its averaged version, before building non asymptotic confidence balls for these estimates, and exhibiting their $L^{p}$ and almost sure rates of convergence.In a second part, we focus on the estimation of the Median Covariation Matrix (MCM), which is a robust dispersion indicator linked to the geometric median. Furthermore, if the studied variable has a symmetric law, this indicator has the same eigenvectors as the covariance matrix. This last property represent a real interest to study the MCM, especially for Robust Principal Component Analysis. We so introduce a recursive algorithm which enables us to estimate simultaneously the geometric median, the MCM, and its $q$ main eigenvectors. We give, in a first time, the strong consistency of the estimators of the MCM, before exhibiting their rates of convergence in quadratic mean.In a third part, in the light of the work on the estimates of the median and of the Median Covariation Matrix, we exhibit the almost sure and $L^{p}$ rates of convergence of averaged stochastic gradient algorithms in Hilbert spaces, with less restrictive assumptions than in the literature. Then, two applications in robust statistics are given: estimation of the geometric quantiles and application in robust logistic regression.In the last part, we aim to fit a sphere on a noisy points cloud spread around a complete or truncated sphere. More precisely, we consider a random variable with a truncated spherical distribution, and we want to estimate its center as well as its radius. In this aim, we introduce a projected stochastic gradient algorithm and its averaged version. We establish the strong consistency of these estimators as well as their rates of convergence in quadratic mean. Finally, the asymptotic normality of the averaged algorithm is given
Elharfaoui, Echarif. "La convergence faible des U-statistiques multivariées pour des processus non stationnaires dépendants". Toulouse 3, 2003. http://www.theses.fr/2003TOU30144.
Yang, Ruiping. "Simulation numérique de diffusion de la lumiére par une goutte pendante par tracé de rayons vectoriels complexes statistiques". Thesis, Normandie, 2019. http://www.theses.fr/2019NORMR143.
This thesis is devoted to the numerical simulation of the scattering of plane wave by a pendent droplet in three dimensions using the Statistic Vectorial Complex Ray Model (SVCRM), which is based on the Vectorial Complex Ray Model (VCRM) developed in the laboratory CORIA. Optical metrology is widely used in many domains of scientific research due to its advantages of being fast and non-intrusive. Numerous measurement techniques have been developed to characterize the size, the temperature, ... of the particles. But most of them are limited to the particles of simple shape because of the lack of theoretical model to predict the relation of the scattered light with the properties of the scatterers, especially for the large non-spherical particle. To overcome this obstacle, the Vectorial Complex Ray Model (VCRM) has been developed. In this model, the wave front curvature is introduced as a new property of light rays. The divergence and the convergence of a wave on the curved surface of the particle can be described easily by the wave front equation. So it can be applied to the scattering of light by large particles of any shape with smooth surface. The VCRM has been validated experimentally and numerically in the cases of scattering in a symmetric plane of scatterer. In order to get over the problem of 2D interpolation with irregular data, Statistic Vectorial Complex Ray Model (SVCRM) is proposed. But the interference phenomena is not considered in its initial version. In this thesis, the method to count the phase due to the optical path, the Fresnel coefficients and the focal liens are carefully studied for a non-spherical particle in the framework of SVCRM. It is then applied to the simulation of the three dimension scattering of a pendent droplet. The scattering patterns around the first and the second order rainbows, in the forward direction are exampled for four typical shapes of pendent droplets obtained experimentally. The results are found in good agreement with experimental scattering patterns. The scattering mechanism and the contribution of different orders of rays are also investigated
Humbert, Ludovic. "Contribution à l'automatisation du traitement des radiographies du système ostéoarticulaire pour la modélisation géométrique et l'analyse clinique". Phd thesis, Paris, ENSAM, 2008. http://pastel.archives-ouvertes.fr/pastel-00004241.
Xu, Hao. "Estimation statistique d'atlas probabiliste avec les données multimodales et son application à la segmentation basée sur l'atlas". Phd thesis, Ecole Polytechnique X, 2014. http://pastel.archives-ouvertes.fr/pastel-00969176.
Decker, Leslie. "Approche alternative à la normalisation et l'évaluation de patrons locomoteurs : application au sprint athlétique". Paris 6, 2006. http://www.theses.fr/2006PA066461.
This research follows on logically from a previous work, of which the originality lays in the methodology used, i. E. The Procrustes method. This method, which was initially designed to allow quantitative analyses of biological shapes using geometric morphometrics, was applied here to an investigation of the "dynamic shapes" created by the spatio-temporal displacements of the runner’s bone-joints during the locomotor cycles. These first studies, which used concepts and methods based on geometric morphometry, provide a new and objective quantitative approach revealing functional differences and similarities among locomotor patterns. In the framework of my doctoral dissertation, the endeavour was to compare behaviors adopted by 100-meter sprinters with different levels of expertise in order to identify possible differences in the way each of these groups manages a race and thus to determine the characteristics of performance in high level sprinting. This investigation, undertaken in close collaboration with the highest ranking French national coaches and athletes, drew on the multivariate exploratory methods and the explanatory predictive techniques to attempt predicting the performance using rhythmical and kinematic parameters collected during the stabilized phase of a 100-meters race. The purpose of this research is to design and validate tools and methods permitting a scientific evaluation of the runner’s motor efficiency. In concrete terms, this has involved the development of a "Memosport" software package allowing the comparison of the measurable and analytical objective data with the qualitative and subjective data supplied by the experts in the field
Fallot, Yann. "Maîtrise de la qualité géométrique des pièces de formes complexes dans le contexte de la continuité numérique". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLN022.
This PhD work is being carried out as part of a CIFRE PhD thesis in collaboration between Safran Aircraft Engines and the LURPA of the ENS Paris-Saclay. Safran Aircraft Engines designs and manufactures engines for civil and military aircraft. In order to meet the high level of global industrial development, Safran Aircraft Engines is constantly seeking to optimize the definitions of its parts while respecting production rate. Tolerancing standards are changing and control methods are improving. The challenge of this work is to control the geometric quality of complex shaped parts in the context of digital continuity.A method is used to establish the links between functions and geometric specifications. In addition, the traceability of dimensional and geometric characteristics is established during the product tolerancing phase.An extension of the CLIC method to components that deform locally is proposed. This extension is integrated into the tolerance method used to establish the links between functions and specifications.An innovative method of generating shape descriptors on surfaces allowing the separation of size, of shape, of position, and of orientation deviations is described in order to achieve a Discrete Modal Decomposition. In addition, the analysis of the results of the Discrete Modal Decomposition applied to thirty complex surfaces allows us to know the repeatability of the manufacturing process
Taillandier, Franck. "Reconstruction de bâti en milieu urbain : une approche multi-vues". Phd thesis, Ecole Polytechnique X, 2004. http://pastel.archives-ouvertes.fr/pastel-00000927.
Zitouna, Souha. "Les valeurs extrêmes dans le cas discret". Paris 6, 1986. http://www.theses.fr/1986PA066255.
Romon, Gabriel. "Contributions to high-dimensional, infinite-dimensional and nonlinear statistics". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAG013.
Three topics are explored in this thesis: inference in high-dimensional multi-task regression, geometric quantiles in infinite-dimensional Banach spaces and generalized Fréchet means in metric trees. First, we consider a multi-task regression model with a sparsity assumption on the rows of the unknown parameter matrix. Estimation is performed in the high-dimensional regime using the multi-task Lasso estimator. To correct for the bias induced by the penalty, we introduce a new data-driven object that we call the interaction matrix. This tool lets us develop normal and chi-square asymptotic distribution results, from which we obtain confidence intervals and confidence ellipsoids in sparsity regimes that are not covered by the existing literature. Second, we study the geometric quantile, which generalizes the classical univariate quantile to normed spaces. We begin by providing new results on the existence and uniqueness of geometric quantiles. Estimation is then conducted with an approximate M-estimator and we investigate its large-sample properties in infinite dimension. When the population quantile is not uniquely defined, we leverage the theory of variational convergence to obtain asymptotic statements on subsequences in the weak topology. When there is a unique population quantile, we show that the estimator is consistent in the norm topology for a wide range of Banach spaces including every separable uniformly convex space. In separable Hilbert spaces, we establish novel Bahadur-Kiefer representations of the estimator, from which asymptotic normality at the parametric rate follows. Lastly, we consider measures of central tendency for data that lives on a network, which is modeled by a metric tree. The location parameters that we study are called generalized Fréchet means: they obtained by relaxing the square in the definition of the Fréchet mean to an arbitrary convex nondecreasing loss. We develop a notion of directional derivative in the tree, which helps us locate and characterize the minimizers. We examine the statistical properties of the corresponding M-estimator: we extend the notion of stickiness to the setting of metrics trees, and we state a non-asymptotic sticky theorem, as well as a sticky law of large numbers. For the Fréchet median, we develop non-asymptotic concentration bounds and sticky central limit theorems
Portefaix, Christophe. "Modélisation des signaux et des images par les attracteurs fractals de systèmes de fonctions itérées (IFS)". Angers, 2004. http://www.theses.fr/2004ANGE0026.
Résumé en anglais
Pellerin, Jeanne. "Prise en compte de la complexité géométrique des modèles structuraux dans des méthodes de maillage fondées sur le diagramme de Voronoï". Phd thesis, Université de Lorraine, 2014. http://tel.archives-ouvertes.fr/tel-01005722.
Bienaise, Solène. "Tests combinatoires en analyse géométrique des données - Etude de l'absentéisme dans les industries électriques et gazières de 1995 à 2011 à travers des données de cohorte". Phd thesis, Université Paris Dauphine - Paris IX, 2013. http://tel.archives-ouvertes.fr/tel-00941220.
Chabani, Arezki. "Analyse méthodologique et caractérisation multi-échelle des systèmes de fractures à l’interface socle/couverture sédimentaire – application à la géothermie (bassin de Valence, SE France)". Electronic Thesis or Diss., Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEM046.
The Valence basin is a graben located in the Rhodanian corridor which belongs to the ECRIS system, and is the subject of many studies due to its geothermal potential. In response to its a multiphase history, fracture networks of the basement and sedimentary cover which are targeted for geothermal exploitation show a complex organization. This study aims to characterize facture networks organization in the Valence basin. It is based on seismic and borehole data in the basin, as well as geological maps, digital elevation model (DEM) and outcrops on the Ardèche margin. Two methodological studies were developed to characterize the orientation and length distributions. These methods allowed to determine fracture network modelling parameters, and highlighted a structural heritage but also a detachment between the basement and the cover
Hullo, Jean-Francois. "Consolidation de relevés laser d'intérieurs construits : pour une approche probabiliste initialisée par géolocalisation". Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00801974.
Mansuy, Mathieu. "Aide au tolérancement tridimensionnel : modèle des domaines". Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00734713.
Da, Silva Sébastien. "Fouille de données spatiales et modélisation de linéaires de paysages agricoles". Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0156/document.
This thesis is part of a partnership between INRA and INRIA in the field of knowledge extraction from spatial databases. The study focuses on the characterization and simulation of agricultural landscapes. More specifically, we focus on linears that structure the agricultural landscape, such as roads, irrigation ditches and hedgerows. Our goal is to model the spatial distribution of hedgerows because of their role in many ecological and environmental processes. We more specifically study how to characterize the spatial structure of hedgerows in two contrasting agricultural landscapes, one located in south-Eastern France (mainly composed of orchards) and the second in Brittany (western France, \emph{bocage}-Type). We determine if the spatial distribution of hedgerows is structured by the position of the more perennial linear landscape features, such as roads and ditches, or not. In such a case, we also detect the circumstances under which this spatial distribution is structured and the scale of these structures. The implementation of the process of Knowledge Discovery in Databases (KDD) is comprised of different preprocessing steps and data mining algorithms which combine mathematical and computational methods. The first part of the thesis focuses on the creation of a statistical spatial index, based on a geometric neighborhood concept and allowing the characterization of structures of hedgerows. Spatial index allows to describe the structures of hedgerows in the landscape. The results show that hedgerows depend on more permanent linear elements at short distances, and that their neighborhood is uniform beyond 150 meters. In addition different neighborhood structures have been identified depending on the orientation of hedgerows in the South-East of France but not in Brittany. The second part of the thesis explores the potential of coupling linearization methods with Markov methods. The linearization methods are based on the use of alternative Hilbert curves: Hilbert adaptive paths. The linearized spatial data thus constructed were then treated with Markov methods. These methods have the advantage of being able to serve both for the machine learning and for the generation of new data, for example in the context of the simulation of a landscape. The results show that the combination of these methods for learning and automatic generation of hedgerows captures some characteristics of the different study landscapes. The first simulations are encouraging despite the need for post-Processing. Finally, this work has enabled the creation of a spatial data mining method based on different tools that support all stages of a classic KDD, from the selection of data to the visualization of results. Furthermore, this method was constructed in such a way that it can also be used for data generation, a component necessary for the simulation of landscapes
Riou-Durand, Lionel. "Theoretical contributions to Monte Carlo methods, and applications to Statistics". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLG006/document.
The first part of this thesis concerns the inference of un-normalized statistical models. We study two methods of inference based on sampling, known as Monte-Carlo MLE (Geyer, 1994), and Noise Contrastive Estimation (Gutmann and Hyvarinen, 2010). The latter method was supported by numerical evidence of improved stability, but no theoretical results had yet been proven. We prove that Noise Contrastive Estimation is more robust to the choice of the sampling distribution. We assess the gain of accuracy depending on the computational budget. The second part of this thesis concerns approximate sampling for high dimensional distributions. The performance of most samplers deteriorates fast when the dimension increases, but several methods have proven their effectiveness (e.g. Hamiltonian Monte Carlo, Langevin Monte Carlo). In the continuity of some recent works (Eberle et al., 2017; Cheng et al., 2018), we study some discretizations of the kinetic Langevin diffusion process and establish explicit rates of convergence towards the sampling distribution, that scales polynomially fast when the dimension increases. Our work improves and extends the results established by Cheng et al. for log-concave densities
Riou-Durand, Lionel. "Theoretical contributions to Monte Carlo methods, and applications to Statistics". Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLG006.
The first part of this thesis concerns the inference of un-normalized statistical models. We study two methods of inference based on sampling, known as Monte-Carlo MLE (Geyer, 1994), and Noise Contrastive Estimation (Gutmann and Hyvarinen, 2010). The latter method was supported by numerical evidence of improved stability, but no theoretical results had yet been proven. We prove that Noise Contrastive Estimation is more robust to the choice of the sampling distribution. We assess the gain of accuracy depending on the computational budget. The second part of this thesis concerns approximate sampling for high dimensional distributions. The performance of most samplers deteriorates fast when the dimension increases, but several methods have proven their effectiveness (e.g. Hamiltonian Monte Carlo, Langevin Monte Carlo). In the continuity of some recent works (Eberle et al., 2017; Cheng et al., 2018), we study some discretizations of the kinetic Langevin diffusion process and establish explicit rates of convergence towards the sampling distribution, that scales polynomially fast when the dimension increases. Our work improves and extends the results established by Cheng et al. for log-concave densities
Vincent, Rémy. "Identification passive en acoustique : estimateurs et applications au SHM". Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT020/document.
Ward identity is a relationship that enables damped linear system identification, ie the estimation its caracteristic properties. This identity is used to provide new observation models that are available in an estimation context where sources are uncontrolled by the user. An estimation and detection theory is derived from these models and various performances studies areconducted for several estimators. The reach of the proposed methods is extended to Structural Health Monitoring (SHM), that aims at measuring and tracking the health of buildings, such as a bridge or a sky-scraper for instance. The acoustic modality is chosen as it provides complementary parameters estimation to the state of the art in SHM, such as structural and geometrical parameters recovery. Some scenarios are experimentally illustrated by using the developed algorithms, adapted to fit the constrains set by embedded computation on anautonomous sensor network
Da, Silva Sébastien. "Fouille de données spatiales et modélisation de linéaires de paysages agricoles". Electronic Thesis or Diss., Université de Lorraine, 2014. http://docnum.univ-lorraine.fr/prive/DDOC_T_2014_0156_DA_SILVA.pdf.
This thesis is part of a partnership between INRA and INRIA in the field of knowledge extraction from spatial databases. The study focuses on the characterization and simulation of agricultural landscapes. More specifically, we focus on linears that structure the agricultural landscape, such as roads, irrigation ditches and hedgerows. Our goal is to model the spatial distribution of hedgerows because of their role in many ecological and environmental processes. We more specifically study how to characterize the spatial structure of hedgerows in two contrasting agricultural landscapes, one located in south-Eastern France (mainly composed of orchards) and the second in Brittany (western France, \emph{bocage}-Type). We determine if the spatial distribution of hedgerows is structured by the position of the more perennial linear landscape features, such as roads and ditches, or not. In such a case, we also detect the circumstances under which this spatial distribution is structured and the scale of these structures. The implementation of the process of Knowledge Discovery in Databases (KDD) is comprised of different preprocessing steps and data mining algorithms which combine mathematical and computational methods. The first part of the thesis focuses on the creation of a statistical spatial index, based on a geometric neighborhood concept and allowing the characterization of structures of hedgerows. Spatial index allows to describe the structures of hedgerows in the landscape. The results show that hedgerows depend on more permanent linear elements at short distances, and that their neighborhood is uniform beyond 150 meters. In addition different neighborhood structures have been identified depending on the orientation of hedgerows in the South-East of France but not in Brittany. The second part of the thesis explores the potential of coupling linearization methods with Markov methods. The linearization methods are based on the use of alternative Hilbert curves: Hilbert adaptive paths. The linearized spatial data thus constructed were then treated with Markov methods. These methods have the advantage of being able to serve both for the machine learning and for the generation of new data, for example in the context of the simulation of a landscape. The results show that the combination of these methods for learning and automatic generation of hedgerows captures some characteristics of the different study landscapes. The first simulations are encouraging despite the need for post-Processing. Finally, this work has enabled the creation of a spatial data mining method based on different tools that support all stages of a classic KDD, from the selection of data to the visualization of results. Furthermore, this method was constructed in such a way that it can also be used for data generation, a component necessary for the simulation of landscapes
Meyer, Valentine. "Apport de la reconstruction virtuelle du bassin Regourdou 1 (Dordogne, France) à la connaissance des mécaniques obstétricales néandertaliennes". Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-01059802.
Sango, Joel. "Sur les tests de type diagnostic dans la validation des hypothèses de bruit blanc et de non corrélation". Thèse, 2016. http://hdl.handle.net/1866/18382.
In statistical modeling, we assume that the phenomenon of interest is generated by a model that can be fitted to the observed data. The part of the phenomenon not explained by the model is called error or innovation. There are two parts in the model. The main part is supposed to explain the observed data, while the unexplained part which is supposed to be negligible is also called error or innovation. In order to simplify the structures, the model are often assumed to rely on a finite set of parameters. The quality of a model depends also on the parameter estimators and their properties. For example, are the estimators relatively close to the true parameters ? Some questions also address the goodness-of-fit of the model to the observed data. This question is answered by studying the statistical and probabilistic properties of the innovations. On the other hand, it is also of interest to evaluate the presence or the absence of relationships between the observed data. Portmanteau or diagnostic type tests are useful to address such issue. The thesis is presented in the form of three projects. The first project is written in English as a scientific paper. It was recently submitted for publication. In that project, we study the class of vector multiplicative error models (vMEM). We use the properties of the Generalized Method of Moments to derive the asymptotic distribution of sample autocovariance function. This allows us to propose a new test statistic. Under the null hypothesis of adequacy, the asymptotic distributions of the popular Hosking-Ljung-Box (HLB) test statistics are found to converge in distribution to weighted sums of independent chi-squared random variables. A generalized HLB test statistic is motivated by comparing a vector spectral density estimator of the residuals with the spectral density calculated under the null hypothesis. In the second project, we derive the asymptotic distribution under weak dependence of cross covariances of covariance stationary processes. The weak dependence is defined in term of the limited effect of a given information on future observations. This recalls the notion of stability and geometric moment contraction. These conditions of weak dependence defined here are more general than the invariance of conditional moments used by many authors. A test statistic based on cross covariances is proposed and its asymptotic distribution is established. In the elaboration of the test statistics, the covariance matrix of the cross covariances is obtained from a vector autoregressive procedure robust to autocorrelation and heteroskedasticity. Simulations are also carried on to study the properties of the proposed test and also to compare it to existing tests. In the third project, we consider a cointegrated periodic model. Periodic models are present in the domain of meteorology, hydrology and economics. When modelling many processes, it can happen that the processes are just driven by a common trend. This situation leads to spurious regressions when the series are integrated but have some linear combinations that are stationary. This is called cointegration. The number of stationary linear combinations that are linearly independent is called cointegration rank. So, to model the real relationship between the processes, it is necessary to take into account the cointegration rank. In the presence of periodic time series, it is called periodic cointegration. It occurs when time series are periodically integrated but have some linear combinations that are periodically stationary. A two step estimation method is considered. The first step is the full rank estimation method that ignores the cointegration rank. It provides initial estimators to the second step estimation which is the reduced rank estimation. It is non linear and iterative. Asymptotic properties of the estimators are also established. In order to check for model adequacy, portmanteau type tests and their asymptotic distributions are also derived and their asymptotic distribution are studied. Simulation results are also presented to show the behaviour of the proposed test.
Atchadé, Yves F. "Quelques contributions sur les méthodes de Monte Carlo". Thèse, 2003. http://hdl.handle.net/1866/14581.