All Years Seminars
[INMA] 2008-11-04 (14.00) : "Unsupervised methods for multivariate data analysis"
At Euler
Speaker :
Cosmin LAZAR (University Reims, France)
Abstract : Multivariate data analysis gathers efficient tools for extracting reliable information in order to comprehend the phenomenon in study. Gathering data into groups or classes according to some similarity criteria is an essential step in the analysis. Intrinsic dimension or dimension reduction of multivariate data, the choice of the similarity criterion, cluster validation are problems which still let open questions.
This work tries to make a step further concerning two of the problems mentioned above: the choice of the similarity measure for data clustering and the dimension reduction of multivariate data. The choice of the similarity measure for data clustering is investigated from the concentration phenomenon of metrics point of view. Non Euclidean metrics are tested as alternative to the classical Euclidian distance as similarity measure. We tested if less concentrated metrics are more discriminative for multivariate data clustering. We also proposed indices which take into account the inter-classes distance (e.g. Davies-Bouldin index) in order to find the optimal metric when the classes are supposed to be Gaussian.
Blind Source Separation (BSS) methods are also investigated for dimension reduction of multivariate data. A BSS method based on a geometrical interpretation of the linear mixing model is proposed. BSS methods which take into account application constraints are used for dimension reduction in two different applications of multivariate imaging. These methods allow the extraction of meaningful factors from the whole data set; they also allow reducing the complexity and the computing time of the clustering algorithms which are used further in analysis.
[INMA] 2008-10-28 (14.00) : "Applications of Real Rational Modules in System Identification"
At Euler
Speaker :
Ivanov, Tzvetan
Abstract : We introduces a real rational module framework in the context of Prediction Error Identification using Box-Jenkins model structures. This module framework, which can easily be extended to other model structures, allows us to solve and/or extend a number of problems related to the computation of error norms that arise in system identification. Our main contribution to system identification is an extension of the asymptotic variance formulas for Box-Jenkins models derived by Ninness and Hjalmarsson to asymptotic auto-covariance with respect to frequency. This auto-covariance is in fact the integral kernel reproducing the tangent space of the model manifold at the true (or fixed) system w.r.t. the Fisher-information metric. We show how to exploit the fact that the tangent space forms a rational module in order to quantify this kernel in terms of the poles and zeros of the true system and the input spectrum.
[INMA] 2008-10-21 (14.00) : "Quelques méthodes pour étudier la contrôlabilité des équations aux dérivées partielles non linéaires."
At Euler
Speaker :
Jean-Michel Coron (Université de Paris-Sud)
Abstract : Quand on veut regarder la contrôlabilité locale autour d'un point
d'équilibre d'un système de contrôle non linéaire modélisé par une
équation aux dérivées partielles, on commence, comme en dimension finie,
par regarder la contrôlabilité du linéarisé. Mais, déjà, à cause d'un
problème de ``pertes de dérivées'', des difficulté apparaissent souvent
pour déduire de la contrôlabilité du linéarisé la contrôlabilité locale
du non linéaire. De plus si le linéarisé n'est pas contrôlable on ne
peut rien déduire pour la contrôlabilité du système non linéaire. Les
méthodes utilisant les crochets de Lie itérés pour traiter ce dernier
cas en dimension finie marchent mal pour les équations aux dérivées
partielles. On présentera d'autres méthodes utiles pour traiter ce cas
(méthode du retour, déformation quasi-statiques, développement en
série). On donnera des exemples récemment traités par ces méthodes.
[INMA] 2008-10-14 (14.00) : "Plane geometry and convexity of polynomial stability regions"
At Euler
Speaker :
Didier HENRION (LAAS-CNRS, University of Toulouse, France, and Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic )
Abstract : The set of controllers stabilizing a linear system is generally non-convex in the parameter space. In the case of two-parameter controller design (e.g. PI control or static output feedback with one input and two outputs), we observe however that quite often for benchmark problem instances, the set of stabilizing controllers seems to be convex. In this note we use elementary techniques from real algebraic geometry (resultants and B´ezoutian matrices) to explain this phenomenon. As a byproduct, we derive a convex linear matrix inequality (LMI) formulation of two-parameter fixed-order controller design problem, when possible.
[INMA] 2008-10-08 (11.45) : D.H.C. - "Decentralized Detection"
At Place Croix du Sud (SUD19)
Speaker :
Tsitsiklis, John
Abstract : Doctor Honoris Causa - Wednesday, October 8th
Seminars
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