Abstract
Understanding how neurons communicate and coordinate their activity is essential for unraveling the brain’s complex functionality. To analyze the intricate spatiotemporal dynamics of neural signaling, we developed Geometric Scattering Trajectory Homology (neuro-GSTH), a novel framework that captures time-evolving neural signals and encodes them into low-dimensional representations. GSTH integrates geometric scattering transforms, which extract multiscale features from brain signals modeled on anatomical graphs, with t-PHATE, a manifold learning method that maps the temporal evolution of neural activity. Topological descriptors from computational homology are then applied to characterize the global structure of these neural trajectories, enabling the quantification and differentiation of spatiotemporal brain dynamics.
We demonstrate the power of neuro-GSTH in neuroscience by applying it to both simulated and biological neural datasets. First, we used neuro-GSTH to analyze neural oscillatory behavior in the Kuramoto model, revealing its capacity to track the synchronization of neural circuits as coupling strength increases. Next, we applied neuro-GSTH to neural recordings from the visual cortex of mice, where it accurately reconstructed visual stimulus patterns such as sinusoidal gratings. Neuro-GSTH-derived neural trajectories enabled precise classification of stimulus properties like spatial frequency and orientation, significantly outperforming traditional methods in capturing the underlying neural dynamics. These findings demonstrate that neuro-GSTH effectively identifies neural motifs—distinct patterns of spatiotemporal activity—providing a powerful tool for decoding brain activity across diverse tasks, sensory inputs, and neurological disorders. Neuro-GSTH thus offers new insights into neural communication and dynamics, advancing our ability to map and understand complex brain functions.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
↵† Co-first authors
Revised to focus on applications to neuroscience data