Engineering Positive Semidefinite Kernels for Trees A Framework and a Survey

Abstract

This paper proposes two frameworks to be used in engineering tree kernels. One is to ensure that the resulting tree kernels be positive semidefinite, while the other is for efficient algorithms to compute the kernels based on the dynamic programming. The first framework provides a method to construct tree kernels using primitive kernels for simpler structures (e.g. for labels, strings) as building blocks and a easy-to-check sufficient condition for the resultant tree kernels to be positive semidefinite. The second framework provides a set of templates of algorithms to calculate a wide range of tree kernels in O(|X|3) or O(|X|2)-time, where |X| denotes the number of vertices of trees.