A new compositional kernel method for multiple kernels

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Most multiple kernels methods try to average out the kernel matrices in one way or another. There is a risk, however, of losing information in the original kernel matrices. We propose here a compositional method for multiple kernels. The new composed kernel matrix is an extension and union of the original kernel matrices. Generally, multiple kernels approaches relied heavily on the training data and had to learn some weights to indicate the importance of each kernel. Our compositional method avoids learning any weight and the importance of the kernel functions are directly derived in the process of learning kernel machines. The performance of the proposed compositional kernel method is illustrated by some experiments in comparison with single kernel.