A contextual normalised edit distance

In order to better fit a variety of pattern recognition problems over strings, using a normalised version of the edit or Levenshtein distance is considered to be an appropriate approach. The goal of normalisation is to take into account the lengths of the strings. We define a new normalisation, contextual, where each edit operation is divided by the length of the string on which the edit operation takes place. We prove that this contextual edit distance is a metric and that it can be computed through an extension of the usual dynamic programming algorithm for the edit distance. We also provide a fast heuristic which nearly always returns the same result and we show over several experiments that the distance obtains good results in classification tasks and has a low intrinsic dimension in comparison with other normalised edit distances.