Geodesic-based distance reveals nonlinear topological features in neural activity from mouse visual cortex.

Area of Science:

• Computational neuroscience
• Topology
• Data analysis

Background:

• Neural data analysis often models activity patterns on manifolds.
• Persistent homology identifies manifold topology, offering insights into neural network function.
• Standard methods struggle with highly nonlinear manifolds due to distance metric limitations.

Purpose of the Study:

• To address the limitations of Euclidean distance in persistent homology for nonlinear neural manifolds.
• To introduce and validate the use of geodesic distance for improved topological analysis of neural data.
• To explore the application of this enhanced method to real neural recordings.

Main Methods:

• Developed a persistent homology approach using geodesic distance estimation.
• Utilized a toy model (circular manifold) to demonstrate metric-dependent performance.
• Investigated method robustness with varying samples, curvature, and noise levels.
• Applied the method to mouse visual cortex neural data (Visual Coding-Neuropixels dataset).

Main Results:

• Euclidean distance can fail to capture true distances on nonlinear manifolds, hindering persistent homology.
• Geodesic distance provides a better approximation, enabling successful identification of complex topological features.
• The method's robustness was confirmed across various manifold properties.
• Analysis of neural data revealed distinct topological features in different cortical regions and under varying stimuli.

Conclusions:

• Geodesic distance is crucial for accurate persistent homology analysis of complex neural manifolds.
• Topological changes in neural manifolds correlate with stimulus properties and cortical regions.
• This approach offers a novel way to interpret neural data and understand visual computation in the brain.