Topological Data Analysis of Clostridioides difficile Infection and Fecal Microbiota Transplantation

TL;DR

This paper applies persistent homology, a topological data analysis method, to DNA sequences from patients with C. difficile infection treated with fecal microbiota transplantation, revealing patterns and visualizations of the data.

Contribution

It introduces the use of persistent homology and persistence landscapes for analyzing DNA sequences in a clinical microbiology context, demonstrating their effectiveness.

Findings

Detection of interesting patterns among patients and donors.

Visualization of DNA sequences as clusters and loops.

Application of topological methods to clinical microbiology data.

Abstract

Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a single index, and is able to capture higher order features beyond the usual clustering techniques. There are three descriptive statistics of persistent homology, namely barcode, persistence diagram and more recently, persistence landscape. Persistence landscape is useful for statistical inference as it belongs to a space of $p-$integrable functions, a separable Banach space. We apply tools in both computational topology and statistics to DNA sequences taken from Clostridioides difficile infected patients treated with an experimental fecal microbiota transplantation. Our statistical and topological data analysis are able to detect interesting patterns among patients and donors. It also provides visualization of DNA sequences in the form of clusters and loops.