Multiresolution topological data analysis for robust activity tracking

Multidimensional sensors represent an increasingly popular, yet challenging data source in modern statistics. Using tools from the emerging branch of Topological Data Analysis (TDA), we address two issues frequently encountered when analysing sensor data, namely their (often) high dimension and their sensibility to the reference system. We show how topological invariants provide a tool for detecting change--points which is robust with respect to both the time resolution we consider and the sensor placement.