This master's thesis results from a request of Cenaero. This work is concerned with the theoretical study of classification and regression methods by Support Vector Machines in order to expand the range of models available in Minamo. The SVM's methods are new techniques of the statistical learning theory proposed by Vapnick in 1995 and developed from the Structural Risk Minimization theory.
The approximation of unknown functions is one of the most frequent use of SVM. The context of this problem is to determine an unknown function relating a set of input and output vectors. The inductive principle of SVM consists in mapping, using kernels, the input vectors into a high-dimensional feature space. In this master's thesis, we study the technique of constructing a hyperplane allowing, in the case of regression, to construct a model wich minimizes the error between the model's output vectors and the true output vecdtors.
The models obtained via the support vector machines for regression can be used to speed up optimization procedures. Indeed, simulations are generally expensive in calculation time and the use of models reduces the number of exacts simulations during the optimization process.
Within the framework of the partnership agreement with Cenaero, we have analyzed and implemented the SMO algorithm which allows to construct SVM models for regression.
Numerical results follow the proposed SVM method for regression and indicate that they are as competitive as other RBF classical methods. Moreover, the SVM's model has been tested and validated after comparison of different models for an industrial test case.
Etude et implémentation des machines à vecteurs de support
Baetmans, F. (Author). 31 Aug 2010
Student thesis: Master types › Master in Mathematics