Robustness of topological persistence in knowledge distillation for wearable sensor data

Topological data analysis (TDA) has shown great success in various applications involving wearable sensor data. However, there are difficulties in leveraging topological features in machine learning and wearable sensors because of the large time consumption and computational resources required to extract the features. To address this problem, knowledge distillation (KD) is utilized to generate a small model and accommodate topological features with persistence image (PI) representations from the raw time series data. Deploying topological knowledge in KD enables the student to achieve better performance compared to the one trained solely on raw time series data. However, it is not yet known if there are coherent characteristics for topological features in PI, which can aid in improving the performance during KD. In this paper, we investigate the suitability and challenges of utilizing topological features in KD for wearable sensor data, thereby contributing to the advancement of the field. Our study explores the impact of transferred topological features by comparing the Teacher-to-Student framework with Multiple Teachers-to-Student where teachers utilize both time series data and persistence images obtained by TDA as inputs. Additionally, we conduct a rigorous examination of topological knowledge effects by testing under various corruptions, knowledge types, and learning strategies in the context of human activity recognition tasks. Our analysis of topological features in KD presents the optimal strategy for incorporating these features. This study includes datasets of varying scales, window lengths, and activity classes, providing a comprehensive evaluation. Our results demonstrate that leveraging topological features in KD to enhance performance across databases.