Phase & Power in Genomic Harmonic Analysis

Genomic Fourier series are produced by applying the Fourier transform to encoded genomic sequences. In the past, the Fourier coefficients of genomic signals were shown to provide useful information in common bioinformatic operations, including sequence alignment (MAFFT) [1], phylogeny construction [2], coding region differentiation [3], and more [4]. In this paper, I apply the phase and power spectra to clustering tasks separately and together. I show that the phase spectra when computed and treated in a way similar to how the power spectra are treated in previous work provides some consistency in the produced genomic sequence clusters (in terms of the location of submission of the original sequences). Clusters are visualized using T-SNE and UMAP procedures, as well as a filtering technique followed by PCA bi-plots. These show well differentiated regional groups, but not consistent global distances between groups. An experiment where distances formed as a composition of phase/power spectra shows that dendrograms produced by the distances which were more heavily weighted on the phase appeared to have lower internal distances within produced cluster. In conclusion, I offer thoughts on the utility of the phase spectra over and in addition to the power spectra for clustering sequences, and notes on the current and future directions associated with this project.