Statistical Learning Algorithm for Tree Similarity

Abstract

Tree edit distance is one of the most frequently used distance measures for comparing trees. When using the tree edit distance, we need to determine the cost of each operation, but this is a labor-intensive and highly skilled task. This paper proposes an algorithm for learning the costs of tree edit operations from training data consisting of pairs of similar trees. To formalize the cost learning problem, we define a probabilistic model for tree alignment that is a variant of tree edit distance. Then, the parameters of the model are estimated using the expectation maximization (EM) technique. In this paper, we develop an algorithm for parameter learning that is polynomial in time (O{mn2d6)) and space (O{n2d4)) where n, d, and m represent the size of the trees, the maximum degree of trees, and the number of training pairs of trees, respectively.