Table of frequently-used mathematical notation.

One of the goals of precision medicine is to classify patients into subgroups that differ in their susceptibility and response to a disease, thereby enabling tailored treatments for each subgroup. Therefore, there is a great need to identify distinctive clusters of patients from patient data. There are three key challenges to three key challenges of patient stratification: 1) the unknown number of clusters, 2) the need for assessing cluster validity, and 3) the clinical interpretability. We developed MapperPlus, a novel unsupervised clustering pipeline, that directly addresses these challenges. It extends the topological Mapper technique and blends it with two random-walk algorithms to automatically detect disjoint subgroups in patient data. We demonstrate that MapperPlus outperforms traditional agnostic clustering methods in key accuracy/performance metrics by testing its performance on publicly available medical and non-medical data set. We also demonstrate the predictive power of MapperPlus in a medical dataset of pediatric stem cell transplant patients where a number of cluster is unknown. Here, MapperPlus stratifies the patient population into clusters with distinctive survival rates. The MapperPlus software is open-source and publicly available.