Topological Nonlinear Analysis of Dynamical Systems in Wearable Sensor-Based Human Physical Activity Inference

This work presents a topological nonlinear analysis approach for dynamical system measurements, frequently appearing in sensor-based inference tasks in human physical activity analysis. Traditional approaches to dynamical modeling included linear and nonlinear methods with specific representational abilities and some drawbacks. A novel approach we investigate is using topological descriptors of the shape of the dynamical attractor to represent the nature of dynamics. The proposed framework has three essential advantages compared to previous approaches: 1) with nonlinear phase space reconstruction, the dynamics descriptor is derived from the observation time series without any statistical assumption; 2) with the topological data analysis technique, the phase space topological properties are described in an intrinsic multiresolution analytical way, which brings novel information compared to traditional phase-space modeling techniques; 3) with different types of measurement sensing signals, the proposed approach shows stability in activities state inference. We illustrate our idea with the physical activity recognition tasks with wearable sensors, where the topological characteristics of reconstructed phase state space show strong representational ability for activity type inference.