Computing the Cyclic Edit Distance for Pattern Classification by Ranking Edit Paths

Abstract

Abstract. The cyclic edit distance between two strings A and B of lengths m and n is the minimum edit distance between A and every cyclic shift of B. This can be applied, for instance, in classification tasks where strings represent the contour of objects. Bunke and Bühler proposed an algorithm that approximates the cyclic edit distance in time O(mn). In this paper we show how to apply a technique for ranking the K shortest paths to an edit graph underlying the Bunke and Bühler algorithm to obtain the exact solution. This technique, combined with pruning rules, leads to an efficient and exact procedure for nearest-neighbour classification based on cyclic edit distances. Experimental results show that the proposed method can be used to classify handwritten digits using the exact cyclic edit distance with only a small increase in computing time with respect to the original Bunke and Bühler algorithm.

Interactive Reconstruction of Archaeological Fragments in a Collaborative Environment

“…Because the contour of a fragment typically has eroded, and because a fragment is often incomplete because tiny pieces are not collectable (or destroyed in collection or simply not found) a suitable string-matching algorithm should not only tolerate mis-matching an individual character but also omitting a portion of the string. Cyclic edit distance, proposed by Marzal et al [10,5], has the ability to measure the similarity of two arbitrary strings that satisfy this criterion. Our approach uses these advantages to estimate the similarity of two cyclic strings in a robust manner.…”

“…Peris et al [5] devised a new algorithm that finds the exact edit distance in a modified edit graph by using Kth shortest paths. The algorithm meliorates the performance from O(|x||y|log(|x|)) to O(|x||y| + K(|x| + |y|)).…”