This paper focuses on learning recognition systems able to cope with sequential data for classification and segmentation tasks. It investigates the integration of discriminant power in the learning of generative models, which are usually used for such data. Based on a procedure that transforms a sample data into a generative model, learning is viewed as the selection of efficient component models in a mixture of generative models. This may be done through the learning of a support vector machine. We propose a few kernels for this and report experimental results for classification and segmentation tasks.