Evaluating the statistical similarity of neural network activity and connectivity via eigenvector angles

Area of Science:

• Computational Neuroscience
• Network Science
• Statistical Analysis

Background:

• Comparing multiple neural networks is crucial for understanding complex systems.
• Existing methods may not fully capture structural similarities between neural network matrices.
• The relationship between neural activity and connectivity requires robust quantitative analysis.

Purpose of the Study:

• To introduce a novel statistical test, the eigenangle test, for comparing matrices representing neural networks.
• To quantify the similarity between correlation matrices of neural activity and connectivity.
• To explore the application of this test to adjacency matrices for network comparison.

Main Methods:

• The eigenangle test quantifies matrix similarity using the angles between their ranked eigenvectors.
• Stochastic models of correlated spiking activity were used to calibrate the test for correlation matrices.
• Comparison with classical two-sample tests like Kolmogorov-Smirnov distance was performed.

Main Results:

• The eigenangle test effectively evaluates structural aspects of pairwise measures in neural networks.
• It provides a unified metric to explore the relationship between connectivity and activity.
• Application to a random balanced network model demonstrated its ability to gauge connectivity influence on activity.

Conclusions:

• The eigenangle test offers a powerful tool for comparing neural network matrices.
• It facilitates quantitative exploration of the interplay between neural connectivity and activity.
• Potential applications include simulation experiments, model validation, and neuroscientific data analysis.