  In this paper, the framework of kernel machines with two layers is
introduced, generalizing classical kernel methods. The new learning methodology
provide a formal connection between computational architectures with multiple
layers and the theme of kernel learning in standard regularization methods.
First, a representer theorem for two-layer networks is presented, showing that
finite linear combinations of kernels on each layer are optimal architectures
whenever the corresponding functions solve suitable variational problems in
reproducing kernel Hilbert spaces (RKHS). The input-output map expressed by
these architectures turns out to be equivalent to a suitable single-layer
kernel machines in which the kernel function is also learned from the data.
Recently, the so-called multiple kernel learning methods have attracted
considerable attention in the machine learning literature. In this paper,
multiple kernel learning methods are shown to be specific cases of kernel
machines with two layers in which the second layer is linear. Finally, a simple
and effective multiple kernel learning method called RLS2 (regularized least
squares with two layers) is introduced, and his performances on several
learning problems are extensively analyzed. An open source MATLAB toolbox to
train and validate RLS2 models with a Graphic User Interface is available.
