Advertisement

Bulletin of Mathematical Biology

, Volume 46, Issue 2, pp 327–332 | Cite as

Properties of levenshtein metrics on sequences

  • William H. E. Day
Article

Abstract

Levenshtein dissimilarity measures are used to compare sequences in application areas including coding theory, computer science and macromolecular biology. In general, they measure sequence dissimilarity by the length of a shortest weighted sequence of insertions, deletions and substitutions required, to transform one sequence into another. Those Levenshtein dissimilarity measures based on insertions and deletions are analyzed by a model involving valuations on a partially ordered set. The model reveals structural relationships among poset, valuation and dissimilarity measure. As a consequence, certain Levenshtein dissimilarity measures are shown to be metrics characterized by betweenness properties and computable in terms of well-known measures of sequence similarity.

Keywords

Dissimilarity Measure Elementary Operation Longe Common Subsequence Lower Valuation Transitive Binary Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Boland, R. P., E. K. Brown and W. H. E. Day. 1983. “Approximating Minimum-length-sequence Metrics: a Cautionary Note.”Math. Social Sci. 4, 261–270.MATHMathSciNetCrossRefGoogle Scholar
  2. Boorman, S. A. and P. Arabie. 1972. “Structural Measures and the Method of Sorting.” InMultidimensional Scaling, Vol. 1, Theory, Eds R. N. Shepard, A. K. Rommey and S. B. Nerlove, pp. 225–249. New York: Seminar Press.Google Scholar
  3. —, and D. C. Olivier. 1973. “Metrics on Spaces of Finite Trees.”J. math. Psychol. 10, 26–59.MATHMathSciNetCrossRefGoogle Scholar
  4. Bunke, H. 1983. “What is the Distance Between Graphs?”Bull. Eur. Assoc. theor. Comput. Sci. No. 20, 35–39.Google Scholar
  5. Day, W. H. E. 1981. “The Complexity of Computing Metric Distances Between Partitions.”Math. Social Sci. 1, 269–287.MATHMathSciNetCrossRefGoogle Scholar
  6. Flament, C. 1963.Applications of Graph Theory to Group Structure. Englewood Cliffs, NJ, Prentice-Hall.Google Scholar
  7. Goodman, N. 1951.The Structure of Appearance. Cambridge MA: Harvard University Press.Google Scholar
  8. Kruskal, J. B. 1983. “An Overview of Sequence Comparison: Time Warps, String Edits, and Macromolecules.”SIAM Rev. 25, 201–237.MATHMathSciNetCrossRefGoogle Scholar
  9. Levenshtein, V. I. 1966. “Binary Codes Capable of Correcting Deletions, Insertions, and Reversals.”Soviet Phys. Dok. 10, 707–710.MathSciNetGoogle Scholar
  10. Lowrance, R. and R. A. Wagner. 1975. “An Extension of the String-to-string Correction Problem.”J. Assoc. Comput. Mach. 22, 177–183.MATHMathSciNetGoogle Scholar
  11. Masek, W. J. and M. S. Paterson. 1983. “How to Compute String Edit Distances Quickly” InTime Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Eds D. Sankoff and J. B. Kruskal, pp. 337–349. Reading, MA: Addison-Wesley.Google Scholar
  12. Monjardet, B. 1981. “Metrics on Partially Ordered Sets—a Survey.”Discrete Math. 35, 173–184.MATHMathSciNetCrossRefGoogle Scholar
  13. Needleman, S. B. and C. D. Wunsch. 1970. “A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins.”J. molec. Biol. 48, 443–453.CrossRefGoogle Scholar
  14. Restle, F. 1959. “A Metric and an Ordering on Sets.”Psychometrika 24, 207–220.MATHMathSciNetCrossRefGoogle Scholar
  15. Robinson, D. F. 1971. “Comparison of Labeled Trees with Valency Three.”J. Combin. Theory 11, 105–119.CrossRefGoogle Scholar
  16. Sankoff, D. and J. B. Kruskal, Eds. 1983.Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison. Reading MA: Addison-Wesley.Google Scholar

Copyright information

© Society for Mathematical Biology 1984

Authors and Affiliations

  • William H. E. Day
    • 1
  1. 1.Department of Computer ScienceMemorial University of NewfoundlandSt. John'sCanada

Personalised recommendations