An Information-theoretic approach to dimensionality reduction in data science

Deep structure of DNA for genomic analysis

Recent advances in next generation sequencing, deep networks and other bioinformatic tools have enabled us to mine huge amount of genomic information about living organisms in the post-microarray era. However, these tools do not explicitly factor in the role of the underlying DNA biochemistry (particularly, DNA hybridization) essential to life processes. Here, we focus more precisely on the role that DNA hybridization plays in determining properties of biological organisms at the macro-level. We illustrate its role with solutions to challenging problems in human disease. These solutions are made possible by novel structural properties of DNA hybridization landscapes revealed by a metric model of oligonucleotides of a common length that makes them reminiscent of some planets in our solar system, particularly earth and saturn. They allow a judicious selection of so-called noncrosshybridizing (nxh) bases that offer substantial reduction of DNA sequences of arbitrary length into a few informative features. The quality assessment of the information extracted by them is high because of their very low Shannon Entropy, i.e. they minimize the degree of uncertainty in hybridization that makes results on standard microarrays irreproducible. For example, SNP classification (pathogenic/nonpathogenic) and pathogen identification can be solved with high sensitivity (~77%/100%) and specificity (~92%/100%, respectively) for combined taxa on a sample of over 264 fully coding sequences in whole bacterial genomes and fungal mitochondrial genomes using machine learning (ML) models. These methods can be applied to several other interesting research questions that could be addressed with similar genomic analyses.