Hotspot identification for Mapper graphs

Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of vertices allowing location of regions of special interest. For instance, in many applications, such as precision medicine, Mapper graph has been used to identify unknown compactly localized subareas within the dataset demonstrating unique or unusual behaviours. This task, performed so far by a researcher, can be automatized using hotspot analysis. In this work we propose a new algorithm for detecting hotspots in Mapper graphs. It allows automatizing of the hotspot detection process. We demonstrate the performance of the algorithm on a number of artificial and real world datasets. We further demonstrate how our algorithm can be used for the automatic selection of the Mapper lens functions.