Capturing Spatiotemporal Signaling Patterns in Cellular Data with Geometric Scattering Trajectory Homology

Neural signals are high-dimensional, noisy, and dynamic, making it challenging to extract interpretable features linked to behavior or disease. We introduce Neurospectrum, a framework that encodes neural activity as latent trajectories shaped by spatial and temporal structure. At each timepoint, signals are represented on a graph capturing spatial relationships, with a learnable attention mechanism highlighting important regions. These are embedded using graph wavelets and passed through a manifold-regularized autoencoder that preserves temporal geometry. The resulting latent trajectory is summarized using a principled set of descriptors - including curvature, path signatures, persistent homology, and recurrent networks -that capture multiscale geometric, topological, and dynamical features. These features drive downstream prediction in a modular, interpretable, and end-to-end trainable framework. We evaluate Neurospectrum on simulated and experimental datasets. It tracks phase synchronization in Kuramoto simulations, reconstructs visual stimuli from calcium imaging, and identifies biomarkers of obsessive-compulsive disorder in fMRI. Across tasks, Neurospectrum uncovers meaningful neural dynamics and outperforms traditional analysis methods.