Revealing Hierarchical Structure in Hippocampal Spatial Representation

It was reported that neurons in the CA1 region of the rat hippocampus, mediating spatial perception, represent space according to a non-linear hyperbolic geometry. However, due to the use of Betti curves, the resulting estimates of dimension and curvature significantly vary with the noise model and are prohibitively expensive to compute. Furthermore, Betti curves do not embed the data into a lower dimensional hyperbolic space, which severely limits deeper insight into the underlying hierarchical structures of this system. As an alternative, we use a recently proposed embedding algorithm, Bayesian Hyperbolic Multi-Dimensional Scaling (Bayesian-HMDS), to provide the embedding, obtain robust, precise estimates of dimension and curvature, and validate the results obtained via Betti curves. Specifically, we apply Bayesian-HMDS to the aforementioned system, more efficiently affirming that CA1 neurons represent space according to hyperbolic geometry, via previously intractable data analyses. Furthermore, we report additional insights into the underlying hierarchical structure of the system.