Topological Neural Data Analysis with Behavioral Constraint

Recently, Topological Data Analysis (TDA) has revealed insights into the topological structure of neural population activity. However, existing TDA methods for neural population activity are computationally demanding, noise-sensitive, and sometimes difficult to interpret. We develop a simple and more interpretable analysis approach to infer the topological structure of behaviorally relevant neural response variability. Our approach first maps the neural activity onto firing rate maps of behavioral variables, and then performs analysis based on these rate maps. Application of our method to grid cell recordings demonstrates its effectiveness without sophisticated preprocessing as required in prior methods. Further test of the methods based on synthetic data suggests that our method is more informative of the deviations from standard topological shapes. Our results also point to the importance of joint analysis of the geometry and topology of neural manifolds.