Hierarchical Directed Acyclic Graph Kernel: Methods for Structured Natural Language Data 
 This paper proposes the Hierarchical Directed Acyclic Graph (HDAG) Kernel for structured natural language data . The HDAG Kernel directly accepts several levels of both chunks and their relations , and then efficiently computes the weighed sum of the number of common attribute sequences of the HDAGs . We applied the proposed method to question classification and sentence alignment tasks to evaluate its performance as a similarity measure and a kernel function . The results of the experiments demonstrate that the HDAG Kernel is superior to other kernel functions and baseline methods . 