Eigenangles: evaluating the statistical similarity of neural network activity and connectivity via eigenvector angles
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Code and data repository accompanying the manuscript "Eigenangles: evaluating the statistical similarity of neural network activity and connectivity via eigenvector angles" by Robin Gutzen, Sonja Grün, Michael Denker (2022) https://doi.org/...
Code and data repository accompanying the publication Gutzen et al. 2022 https://doi.org/...
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Keywords
Statistical Testing | Random Matrix Theory | Neural Network Models | Connectivity-Activity Relation
Content
The different applications and testing scenarios of the eigenangle test are separated into the folders balanced_network, stochastic_activity, and polychony_network containing their corresponding workflows (see the respective README.md for details). The top-level folder scripts contains a general code basis used by each of the workflows.
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The folder paper_figures contains the figures from the publications as generated by either notebooks or scripts in the respective application folders. Figure 1, 2, and 3 are produced by the respective notebook with this folder.
The interactive jupyter notebook eigenangle_basics.ipynb presents a step-wise construction and explanation of the eigenangle test and can be executed via the above mybinder badge.
Data
The various comparison results of the applications are stored as pandas dataframes in .csv files.
The folders balanced_network/simulation_output, polychony_network/simulation_output, and stochastic_activity/correlation_matrices contain larger files and are indexed with git annex. git clone only downloads links of these files. To download their content run git annex sync --content, or use the gin client.
The folder paper_figures contains the figures from the publications as generated by either notebooks or scripts in the respective application folders. Figure 1 and 2 are produced by the respective notebook with this folder.
The interactive jupyter notebook eigenangle_basics.ipynb](https://mybinder.org/v2/git/https%3A%2F%2Fgin.g-node.org%2FINM-6%2Feigenangles/HEAD?labpath=eigenangle_basics.ipynb) presents a step-wise construction and explanation of the eigenangle test and can be executed via the above mybinder badge.
refs/remotes/origin/synced/master
Abstract
Neural systems are often represented by networks, and the strategic comparisons between multiple, similar networks is a prevalent task in many research scenarios.
In this study, we construct a statistical test for the comparison of matrices representing pairwise aspects of neural networks, in particular the spiking activity correlation and the connectivity.
The "eigenangle test" is based on quantifying the similarity of two matrices by the angles between their ranked eigenvectors.
We calibrate the test's behavior with stochastic models of correlated spiking activity and demonstrate how it compares to classical two-sample tests, such as the Kolmogorov-Smirnov distance, in that it is able to evaluate also structural aspects of pairwise measures.
The principle of the eigenangle test can be applied to compare both the activity correlations as well as the adjacency matrices of certain types of networks and quantify their similarity with the same metric. Thus, the approach can be used to quantitatively explore the relationship between connectivity and activity.
By applying the eigenangle test to the comparison of weight matrices and correlation matrices of a random balanced network model before and after a specific synaptic rewiring intervention, we gauge the influence of connectivity features onto the correlated activity.
Potential applications of the eigenangle test include theoretical explorations, model validation, and data analysis.
