Weighted Automata Sequence Kernel

Sequence kernels are widely used for learning from sequential data. The literature includes a variety of sequence kernels. In this paper, we present a general framework to deal with sequence kernels, termed weighted automata sequence kernel. In fact, the mapping of a string s to a high dimensional feature space can be modeled by a formal power series that can be realized by a weighted automaton (WA) As representing all subsequences. The computation of the kernel between two strings K(s,t) is the behavior of the WA As,t = As ∩ At. Thus, as formulated, it can be generalized to sequence set kernel. For the kernel computation efficiency, we propose a forward lookup automata intersection technique to prevent non successful ∈-paths while evaluating the WA computations. The experiments use the Reuters-21578 collection. The results reveal that the kernel evaluation using our proposed technique is faster than that using the standard intersection. We also study the relationship between our general framework and a variety of common sequence kernels. Finally, based on our general framework, we describe the essential to create a new sequence-set kernel that can also be seen as a tree kernel.