Functional Medians and Point Process Depths for Clustering Spike Trains

We propose an integrated statistical framework combining point process modeling and functional data analysis for the classification of neuronal activity from calcium imaging. After denoising and spike reconstruction, neuronal signals are analyzed both as temporal point patterns and as smooth functional trajectories. Spike trains are classified using distance-based prototypes and low-dimensional embeddings, while calcium traces are clustered through a depth-based functional approach relying on FPCA and modified band depth. Linking the two representations allows a direct comparison between spike-based and func- tional clusterings, yielding a unified and complementary characterization of neuronal dynamics.