Quaternionic periodicity transform: an algebraic solution to the tandem repeat detection problem.

Motivation: One of the main tasks of DNA sequence analysis is identification of repetitive patterns. DNA symbol repetitions play a key role in a number of applications, including prediction of gene and exon locations, identification of diseases, reconstruction of human evolutionary history and DNA forensics.
Results: A new approach towards identification of tandem repeats in DNA sequences is proposed. The approach is a refinement of previously considered method, based on the complex periodicity transform. The refinement is obtained, among others, by mapping of DNA symbols to pure quaternions. This mapping results in an enhanced, symbol-balanced sensitivity of the transform to DNA patterns, and an unambiguous threshold selection criterion. Computational efficiency of the transform is further improved, and coupling of the computation with the period value is removed, thereby facilitating parallel implementation of the algorithm. Additionally, a post-processing stage is inserted into the algorithm, enabling unambiguous display of results in a convenient graphical format. Comparison of the quaternionic periodicity transform with two well-known pattern detection techniques shows that the new approach is competitive with these two techniques in detection of exact and approximate repeats.