Palestrante: Prof. Adilson Elias Xavier (COPPE/UFRJ)
Título da Palestra: Solving very Large Clustering Problems by Using the Hyperbolic Smoothing Method
Resumo da Palestra:
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Clustering analysis can be done according to numerious criteria, throught different mathematical formulations. The methodology considered details with clustering problems that have a common component: The measure of a distance, which can be done following different metrics.
The methodology, called hyperbolic smooothing, has a wider scope, and can be applied to clustering according to distances measured in different metrics, such as Euclinian, Minkowski, Manhattan and Chebychew norms. By soothing we fundamentally mean the substituation of an intrinsically non-differentiable two -level problem by a comletely differentiable single-level alternative. Ths is achieved through the solution of a sequence of differnentiable sub-problems which gradually approaches to the original problem. An additional improvement considers the partition of the set of observations into two groups: "date om tje frpmtoer" and "data in graviitational regions". The resulting effect is desirable sunbstantial reduction of the computational effort necessary to solve the clustering problems. The talk will consider one particular clustering formulation: Amoung many criteria, the most natural, intuitive and freauently adopted criteria is the minimum sum-of-suares clustering (MSSC); In order to show the distinct performace of proposed methodologies, a set of computational results obtained by solving very large test problems is presented. |
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Short Bio:
Adilson Elias Xavier is a Professor of the Federal University of Rio de Janeiro (UFRJ), whose main interests rely on Mathematical Programming, particularaly Nonlinear Programing in Peanlty and Augmented Lagranging Methods. He earned his D.Sc. on Systems Engineering and Computting aat UFRJ on 1992. He is the author of the Hyperbolic Penalty method for Nonlinear Programing and the Hyperbolic Smoothing modeling technique, which has been applied for solving important non-differentiable problems, such as: covering, packing, clustering or location, having obtained unprecedent computational results, He has been working as consultant in many project with some of the most important Brazilian companies, such as Petrobras, CEPEL, Eletrobas, ONS, Furnas and Embratel. He earmed prizes from SOBRAPO (Brazilian Operations Research Society) and IFORS (International of Operatioinal Reserarch Socities).
