Flexible Tree Kernels based on Counting the Number of Tree Mappings

Functions counting the number of common sub-patterns between trees have been promising candidates for kernel functions for trees in learning systems. There are several viewpoints of how two patterns between two trees can be regarded as the same. In the tree edit distance, these viewpoints have been well formalized as the class of tree mappings, and several distance measures have been proposed according to the classes of tree mappings. In this paper, we address the design problem of new flexible tree kernels corresponding to four representative classes of tree mappings. Therefore, first, we develop four counting functions for tree mappings according to the four classes. Secondly, we prove that three of the four counting functions are kernel functions, and the other is not.