A New Frontier of Kernel Design for Structured Data

Many kernels for discretely structured data in the literature are designed within the framework of the convolution kernel and its generalization, the mapping kernel. The two most important advantages to use this framework are an easy-to-check criteria of positive definiteness of the resulting kernels and efficient computation based on the dynamic programming methodology. On the other hand, the recent theory of partitionable kernels reveals that the known kernels only take advantage of a very small portion of the potential of the framework. In fact, we have good opportunities to find novel and important kernels in the unexplored area. In this paper, we shed light on a novel important class of kernels within the framework: We give a mathematical characterization of the class, and then, based on the characterization, we show a parametric method to optimize kernels of the class to specific problems. Also, we present some experimental results that show that the new kernels are promising in both accuracy and efficiency.