Benchmarking criteria to determine latent linear dimensionality in neural data

Area of Science:

• Neuroscience
• Computational Neuroscience
• Data Science

Background:

• Dimensionality reduction is essential for analyzing large neural recording datasets in neuroscience.
• Principal Component Analysis (PCA) remains a standard technique, but optimal parameter selection is debated.
• Lack of consensus on estimating the number of latent variables hinders reproducible neuroscience research.

Purpose of the Study:

• To evaluate different criteria for selecting the optimal number of latent variables in PCA for neural data.
• To identify robust methods unaffected by data size, noise levels, and matrix properties.
• To provide practical guidance and tools for dimensionality estimation in neuroscience.

Main Methods:

• Simulated neural data were used to test various dimensionality estimation criteria.
• Methods evaluated include Parallel Analysis, Optimal Singular Value Thresholding, and Cross-Validation (CV).
• CV schemes were tested along single and multiple matrix dimensions; performance was compared.

Main Results:

• Parallel Analysis, Optimal Singular Value Thresholding, and CV demonstrated superior performance, robust to noise and unit number.
• Simultaneous cross-validation across feature and observation dimensions yielded the best results, outperforming single-dimension CV.
• Analysis of real neural data from macaque visual cortex showed varying results based on criteria, but consistent dimensionality trends.
• The number of estimable significant components is severely limited by data matrix properties like eigenvalue decay.

Conclusions:

• The definition of 'dimensionality' in neural data requires careful consideration.
• Robust criteria like Parallel Analysis, SVD thresholding, and multi-dimensional CV should be adopted for PCA in neuroscience.
• A provided software package and web app aim to assist researchers in selecting appropriate latent variables.