Multiple kernel learning (MKL) approach has been proposed for kernel methods and has shown high performance for solving some real-world applications. It consists on learning the optimal kernel from one layer of multiple predefined kernels. Unfortunately, this approach is not rich enough to solve relatively complex problems. With the emergence and the success of the deep learning concept, multilayer of multiple kernel learning (MLMKL) methods were inspired by the idea of deep architecture. They are introduced in order to improve the conventional MKL methods. Such architectures tend to learn deep kernel machines by exploring the combinations of multiple kernels in a multilayer structure. However, existing MLMKL methods often have trouble with the optimization of the network for two or more layers. Additionally, they do not always outperform the simplest method of combining multiple kernels (i.e., MKL). In order to improve the effectiveness of MKL approaches, we introduce, in this paper, a novel backpropagation MLMKL framework. Specifically, we propose to optimize the network over an adaptive backpropagation algorithm. We use the gradient ascent method instead of dual objective function, or the estimation of the leave-one-out error. We test our proposed method through a large set of experiments on a variety of benchmark data sets. We have successfully optimized the system over many layers. Empirical results over an extensive set of experiments show that our algorithm achieves high performance compared to the traditional MKL approach and existing MLMKL methods.
