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Related Experiment Videos

A normalized Levenshtein distance metric.

Li Yujian1, Liu Bo

  • 1College of Computer Science and Technology, Beijing University of Technology, Pingleyuan 100, Chaoyang District, Beijing 100022, P.R. China. liyujian@bjut.edu.cn

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 14, 2007
PubMed
Summary
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This study introduces a new normalized edit distance that satisfies the triangle inequality, a crucial property for genuine metrics. This novel string metric offers comparable or improved performance in applications like handwritten digit recognition.

Area of Science:

  • Computer Science
  • Information Theory
  • Computational Linguistics

Background:

  • Existing normalized edit distances often fail to satisfy the triangle inequality, limiting their applicability as true mathematical metrics.
  • The triangle inequality is a fundamental property for a distance measure to be considered a genuine metric.

Purpose of the Study:

  • To define a new normalized edit distance that adheres to the triangle inequality.
  • To ensure the new distance is a valid metric and computationally efficient.

Main Methods:

  • The new normalized edit distance is defined as a function of string lengths and the Generalized Levenshtein Distance (GLD).
  • The computational complexity is O(|X|.|Y|), leveraging the GLD computation.
  • The distance is constrained to be valued in [0, 1] under specific weight function conditions.

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Main Results:

  • The proposed normalized edit distance satisfies the triangle inequality when specific conditions on the weight function are met.
  • Experiments using the AESA algorithm for handwritten digit recognition demonstrated comparable performance to existing methods.
  • The new distance showed potential for slight performance improvements when the triangle inequality is violated in the dataset.

Conclusions:

  • The newly defined normalized edit distance is a genuine metric, fulfilling the triangle inequality.
  • It offers a computationally feasible and effective alternative for string comparison tasks.
  • Its applicability is validated in pattern recognition tasks such as handwritten digit recognition.