New Linear-time Algorithm for SubTree Kernel Computation based on Root-Weighted Tree Automata

Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel computation. First, we introduce a new class of weighted tree automata, called Root-Weighted Tree Automata, and their associated formal tree series. Then we define, from this class, the SubTree automata that represent compact computational models for finite tree languages. This allows us to design a theoretically guaranteed linear-time algorithm for computing the SubTree Kernel based on weighted tree automata intersection. The key idea behind the proposed algorithm is to replace DAG reduction and nodes sorting steps used in previous approaches by states equivalence classes computation allowed in the weighted tree automata approach. Our approach has three major advantages: it is output-sensitive, it is free sensitive from the tree types (ordered trees versus unordered trees), and it is well adapted to any incremental tree kernel based learning methods. Finally, we conduct a variety of comparative experiments on a wide range of synthetic tree languages datasets adapted for a deep algorithm analysis. The obtained results show that the proposed algorithm outperforms state-of-the-art methods.