Topological Data Analysis of DNA sequence data in human gut microbiome

Abstract

Persistent Homology broadly refers to tracking the topological features of a geometric object. This study aims to use persistent homology to explore the effect of Human Biotherapy on patients suffering from Clotridium Difficile Infection. The data is presented in the form of several distance matrices and these are analyzed applying summary statistics of persistent homology, namely barcodes, persistence diagrams and persistence landscapes. It is found that there is a difference in the area under the persistence landscapes before and after treatment in dimensions zero and one. These differences are explored using projection onto lower dimensions using isometric mapping. It is found that there are differences in the number of clusters in dimension zero and the number and length of loops in dimension one.