Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of the algorithm is a graph where nodes represent clusters and edges represent the sharing of data points between two clusters. However, several parameters must be selected before applying Mapper and the resulting graph may vary dramatically with the choice of parameters. We define an intrinsic notion of Mapper instability that measures the variability of the output as a function of the choice of parameters required to construct a Mapper output. Our results and discussion are general and apply to all Mapper-type algorithms. We derive theoretical results that provide estimates for the instability and suggest practical ways to control it. We provide also experiments to illustrate our results and in particular we demonstrate that a reliable candidate Mapper output can be identified as a local minimum of instability regarded as a function of Mapper input parameters.
Data-driven discovery in complex neurological disorders has potential to extract meaningful syndromic knowledge from large, heterogeneous data sets to enhance potential for precision medicine. Here we describe the application of topological data analysis (TDA) for data-driven discovery in preclinical traumatic brain injury (TBI) and spinal cord injury (SCI) data sets mined from the Visualized Syndromic Information and Outcomes for Neurotrauma-SCI (VISION-SCI) repository. Through direct visualization of inter-related histopathological, functional and health outcomes, TDA detected novel patterns across the syndromic network, uncovering interactions between SCI and co-occurring TBI, as well as detrimental drug effects in unpublished multicentre preclinical drug trial data in SCI. TDA also revealed that perioperative hypertension predicted long-term recovery better than any tested drug after thoracic SCI in rats. TDA-based data-driven discovery has great potential application for decision-support for basic research and clinical problems such as outcome assessment, neurocritical care, treatment planning and rapid, precision-diagnosis.