Pattern Recognition of Strings with Substitutions, Insertions, Deletions and Generalized Transpositions1

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 characters2 [LW75] 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.