Computation of Normalized Edit Distance and Applications

Given two strings X and Y over a finite alphabet, the normalized edit distance between X and Y, d( X , Y ) is defined as the minimum of W ( P ) / L ( P ) , where P is an editing path between X and Y , W ( P ) is the sum of the weights of the elementary edit operations of P, and L ( P ) is the number of these operations (length of P). In this paper, it is shown that in general, d ( X , Y ) cannot be computed by first obtaining the conventional (unnormalized) edit distance between X and Y and then normalizing this value by the length of the corresponding editing path. In order to compute normalized edit distances, a new algorithm that can be implemented to work in O(m .n’) time and O(n2) memory space is proposed, where m and n are the lengths of the strings under consideration, and m 2 n. Experiments in hand-writtem digit recognition are presented, revealing that the normalized edit distance consistently provides better results than both unnormalized or post-normalized classical edit distances. Index TemEditing, Levenshtein distance, normalized edit distance, optical character recognition, pattern recognition, speech recognition, spelling correction, string correction,