A Measure of DNA Sequence Dissimilarity Based on Mahalanobis Distance between Frequencies of Words

A number of algorithms exist for searching genetic databases for biologically significant similarities in DNA sequences. Past research has shown that word-based search tools are computationally efficient and can find similarities or dissimilarities invisible to other algorithms like FASTA. We characterize a family of word-based dissimilarity measures that define distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Applications to real data demonstrate that currently used word-based methods that rely on Euclidean distance can be significantly improved by using Mahalanobis distance, which accounts for both variances and covariances between frequencies of n-words. Furthermore, in those cases where Mahalanobis distance may be too difficult to compute, using standardized Euclidean distance, which only corrects for the variances of frequencies of n-words, still gives better performance than the Euclidean distance. Also, a simple way of combining distances obtained at different n-words is considered. The goal is to obtain a single measure of dissimilarity between two DNA sequences. The performance ranking of the preceding three distances still holds for their combined counterparts. All results obtained in this paper are applicable to amino acid sequences with minor modifications.