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A metric normalization of tree edit distance

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Abstract

Traditional normalized tree edit distances do not satisfy the triangle inequality. We present a metric normalization method for tree edit distance, which results in a new normalized tree edit distance fulfilling the triangle inequality, under the condition that the weight function is a metric over the set of elementary edit operations with all costs of insertions/deletions having the same weight. We prove that the new distance, in the range [0, 1], is a genuine metric as a simple function of the sizes of two ordered labeled trees and the tree edit distance between them, which can be directly computed through tree edit distance with the same complexity. Based on an efficient algorithm to represent digits as ordered labeled trees, we show that the normalized tree edit metric can provide slightly better results than other existing methods in handwritten digit recognition experiments using the approximating and eliminating search algorithm (AESA) algorithm.

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Authors and Affiliations

  1. College of Computer Science and Technology, Beijing University of Technology, Beijing, 100124, China

    Yujian Li & Zhang Chenguang

  2. College of Information Science and Technology, Hainan University, Haikou, 570228, China

    Zhang Chenguang

Authors
  1. Yujian Li
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  2. Zhang Chenguang
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Correspondence to Yujian Li.

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Li, Y., Chenguang, Z. A metric normalization of tree edit distance. Front. Comput. Sci. China 5, 119–125 (2011). https://doi.org/10.1007/s11704-011-9336-2

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  • DOI: https://doi.org/10.1007/s11704-011-9336-2

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