Pattern recognition of strings with substitutions, insertions, deletions and generalized transpositions

Abstract

We study the problem of recognizing a string Y which is the noisy version of some unknown string X * chosen from a finite dictionary, H. The traditional case which has been extensively studied in the literature is the one in which Y contains substitution, insertion and deletion (SID) errors. Although some work has been done to extend the traditional set of edit operations to include the straightforward transposition of adjacent characters 2[14] the problem is unsolved when the transposed characters are themselves subsequently substituted, as is typical in cursive and typewritten script, in molecular biology and in noisy chain-coded boundaries. In this paper we present the first reported solution to the analytic problem of editing one string X to another, Y using these four edit operations. A scheme for obtaining the optimal edit operations has also been given. Both these solutions are optimal for the infinite alphabet case. Using these algorithms we present a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors. The paper includes experimental results involving sub-dictionaries of the most common English words which demonstrate the superiority of our system over existing methods.1 Partially supported by the Natural Sciences and Engineering Research Council of Canada. A preliminary version of this paper can be found in the Proceedings of the 1995 IEEE International Conference on Systems, Man and Cybernetics, Vancouver, October 1995, pp. 1154-1159 There has been some recent work done [Oo93] to consider the squashing and expansion operations too, where in the squashing operation two (or more) contiguous characters of X can be transformed into a single character of Y, and in the expansion operation a single character in X may be expanded into two or more contiguous characters of Y.Pat. Recog. with Subst., Insert., Delet.and Gen. Transpos. Errors. Page 2

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