Neighbourhood counting metric for sequences

The longest common subsequence (LCS) is a well known and popular method for measuring similarity between sequences. In this paper we consider all common subsequences (ACS) as a measure of sequence similarity with the view that all common information is captured. ACS is inspired and derived from a generic similarity measure, neighbourhood counting metric (NCM). The close connection of NCM with probability and the Bayes classifier helps gain an insight from the probabilistic perspective into ACS. We also design an algorithm to calculate this measure and carry out an experiment in the framework of k-nearest neighbours on a gene sequence classification task. The experiment shows that ACS and LCS have little difference for small k values, but differ significantly for large k values. ACS's performance remains steady as k gets larger, but LCS's performance drops sharply as k gets larger. Such a property may be useful for some tasks.