Abstract EN:

Kernel methods are providing a ``plug and play'' approach to algorithm design. For instance, Support Vector Machines (SVMs) has been successfully applied to many tasks through simply substituting appropriate kernels. We design several kernels for different kinds of image representations. For global image representations, we propose a general form of the Histogram Intersection kernel by relaxing conditions of its positive definiteness. We propose also a compactly supported kernel (GCS kernel) based on a geometric approach. The compactness property enhances the computation of the SVM training using sparse linear algebra algorithms. For local representations, images are described by local image features such as local jets computed on interest points. We propose is the intermediate matching kernel which defines an alignement between the two sets of local features using a matching set. The latter is learned using local features from all training images. A crucial step after designing kernels is to carefully choose hyperparameters. In this research, we addressed also tuning kernel parameters. First we have been interested by generalization error estimation. We introduce a new estimator for the leave-two-out using the mean-field approach. We prove that the proposed estimator is statistically more robust than the leave-one-out ones. We propose also an optimization scheme (LCCP), based on the concave convex procedure, for tuning kernel parameters. The LCCP is more efficient than gradient descent technique since it insures that the optimization criterion decreases monotonically and converges to a local minimum without searching the size step.