Simple fast algorithms for the editing distance between trees and related problems
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The problem of learning metrics between structured data (strings, trees or graphs) has been the subject of various recent papers. With regard to the specific case of trees, some approaches focused on the learning of edit probabilities required to compute a so-called stochastic tree edit distance. However, to reduce the algorithmic and learning constraints, the deletion and insertion operations are achieved on entire subtrees rather than on single nodes. We aim in this article at filling the gap with the learning of a more general stochastic tree edit distance where node deletions and insertions are allowed. Our approach is based on an adaptation of the EM optimization algorithm to learn parameters of a tree model. We propose an original experimental approach aiming at representing images by a tree-structured representation and then at using our learned metric in an image recognition task. Comparisons with a non learned tree edit distance confirm the effectiveness of our approach.