Evaluation of genome similarities: a wavelet-domain approach

Abstract

The wavelets arised to solve the problems when you work with non-stationary data, signals contaminated with noise, large data volume, detection of self-similarity, separation of components in a signal, among others. The technique called the “wavelet transform” corresponds to one of its main characteristics, because the data (signal, image or function) can be decomposed in the frequency domain as well as in the time domain. The low frequencies (larger scales) correspond to a global information, which generally extends over the analyzed data, while the high frequencies (reduced scales) correspond to more detailed information, which lasts a relatively short period of time. The present work was divided in the presentation of three different genome cluster analysis techniques using wavelets. These techniques were employed in ten sequences of the Mycobacterium tuberculosis genome. The first technique used to grouping the of genomes was the use of energy (variance). This energy was obtained by summing the detail coefficients by the square of each level of decomposition (five levels) of the original signal by means of the Daubechies wavelet with four null moments. As a result, the formation of 3 distinct groups was found. The second technique approached the junction of wavelets with the methodology Elastic net. In this analysis, after obtaining the levels of decomposition using wavelets, the Elastic net was applied at each level, where it was possible to verify the formation of the groups. The results showed that levels 4 and 5 were the ones that presented the best formation of the groups, being found three different groups. The third technique involved the combination of wavelets with the Hurst exponent. From the results obtained of the levels of decomposition by wavelets, using the same configurations of the first and second techniques previously described, the Hurst exponent was calculated for each level of decomposition, using five methods of estimation of the Hurst exponent. Each method presented different group formations, but the method that presented the similar results according to the two previous techniques was the method of aggregate variance.