Algorithme d’apprentissage séquentiel pour la méthode KFD Relations avec la méthode KPCA

In recent years, many detection methods based on the reproducing kernel Hilbert spaces have been developed. The majority of these methods incorporate the fundamental idea used by Vapnik in the Support Vector Machines which consists of extending a linear algorithm for the non-linear case by using the notion of kernels. Kernel Fisher Discriminant (KFD) is one of these methods which leads to competitiveness results in many practical cases. However, use of the KFD method requires storage and handling of matrices of a size equal to that of the number of available examples. This may be critical when the training set is large. This paper presents a sequential algorithm for the KFD method which does not require handling or even the storage of large matrices. In addition, another sequential algorithm, which fulfils the same requirements as that of the KFD algorithm, is presented for the Kernel Principal Component Analysis (KPCA) method which is used to extract non-linear features.