Polynomial-time metrics for attributed trees

IEEE Trans Pattern Anal Mach Intell. 2005 Jul;27(7):1087-99. doi: 10.1109/tpami.2005.146.

Abstract

We address the problem of comparing attributed trees and propose four novel distance measures centered around the notion of a maximal similarity common subtree. The proposed measures are general and defined on trees endowed with either symbolic or continuous-valued attributes and can be applied to rooted as well as unrooted trees. We prove that our measures satisfy the metric constraints and provide a polynomial-time algorithm to compute them. This is a remarkable and attractive property, since the computation of traditional edit-distance-based metrics is, in general, NP-complete, at least in the unordered case. We experimentally validate the usefulness of our metrics on shape matching tasks and compare them with (an approximation of) edit-distance.

Publication types

  • Comparative Study
  • Evaluation Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Artificial Intelligence*
  • Cluster Analysis
  • Computer Simulation
  • Image Interpretation, Computer-Assisted / methods*
  • Information Storage and Retrieval / methods*
  • Models, Statistical*
  • Numerical Analysis, Computer-Assisted
  • Pattern Recognition, Automated / methods*
  • Signal Processing, Computer-Assisted*
  • Time Factors