Properties of levenshtein metrics on sequences
- 80 Downloads
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.
KeywordsDissimilarity Measure Elementary Operation Longe Common Subsequence Lower Valuation Transitive Binary Relation
Unable to display preview. Download preview PDF.
- 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
- Bunke, H. 1983. “What is the Distance Between Graphs?”Bull. Eur. Assoc. theor. Comput. Sci. No. 20, 35–39.Google Scholar
- Flament, C. 1963.Applications of Graph Theory to Group Structure. Englewood Cliffs, NJ, Prentice-Hall.Google Scholar
- Goodman, N. 1951.The Structure of Appearance. Cambridge MA: Harvard University Press.Google Scholar
- 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
- 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