PHEATPRUNER: Interpretable Data-centric Feature Selection for Multivariate Time Series Classification through Persistent Homology

Balancing performance and interpretability in multivariate time series classification is a significant challenge due to data complexity and high dimensionality. This paper introduces PHeatPruner, a method integrating persistent homology and sheaf theory to address these challenges. Persistent homology facilitates the pruning of up to 45% of the applied variables while maintaining or enhancing the accuracy of models such as Random Forest, CatBoost, XGBoost, and LightGBM, all without depending on posterior probabilities or supervised optimization algorithms. Concurrently, sheaf theory contributes explanatory vectors that provide deeper insights into the data's structural nuances. The approach was validated using the UEA Archive and a mastitis detection dataset for dairy cows. The results demonstrate that PHeatPruner effectively preserves model accuracy. Furthermore, our results highlight PHeatPruner's key features, i.e. simplifying complex data and offering actionable insights without increasing processing time or complexity. This method bridges the gap between complexity reduction and interpretability, suggesting promising applications in various fields.