Multi-Fractal Analysis for Feature Extraction from DNA Sequences

Abstract

This paper presents estimations of multi-scale (multi-fractal) measures for feature extraction from deoxyribonucleic acid (DNA) sequences, and demonstrates the intriguing possibility of identifying biological functionality using information contained within the DNA sequence. We have developed a technique that seeks patterns or correlations in the DNA sequence at a higher level than the local base-pair structure. The technique has three main steps: (i) transforms the DNA sequence symbols into a modified Lévy walk, (ii) transforms the Lévy walk into a signal spectrum, and (iii) breaks the spectrum into sub-spectra and treats each of these as an attractor from which the multi-fractal dimension spectrum is estimated. An optimal minimum window size and volume element size are found for estimation of the multi-fractal measures. Experimental results show that DNA is multi-fractal, and that the multi-fractality changes depending upon the location (coding or non-coding region) in the sequence.