Abstract

It is generally accepted that the number of neurons in a given brain area far exceeds the number of neurons needed to carry any specific function controlled by that area. For example, motor areas of the human brain contain tens of millions of neurons that control the activation of tens or at most hundreds of muscles. This massive redundancy implies the covariation of many neurons, which constrains the population activity to a low-dimensional manifold within the space of all possible patterns of neural activity. To gain a conceptual understanding of the complexity of the neural activity within a manifold, it is useful to estimate its dimensionality, which quantifies the number of degrees of freedom required to describe the observed population activity without significant information loss. While there are many algorithms for dimensionality estimation, we do not know which are well suited for analyzing neural activity. The objective of this study was to evaluate the efficacy of several representative algorithms for estimating the dimensionality of linearly and nonlinearly embedded data. We generated synthetic neural recordings with known intrinsic dimensionality and used them to test the algorithms’ accuracy and robustness. We emulated some of the important challenges associated with experimental data by adding noise, altering the nature of the embedding of the low-dimensional manifold within the high-dimensional recordings, varying the dimensionality of the manifold, and limiting the amount of available data. We demonstrated that linear algorithms overestimate the dimensionality of nonlinear, noise-free data. In cases of high noise, most algorithms overestimated the dimensionality. We thus developed a denoising algorithm based on deep learning, the “Joint Autoencoder”, which significantly improved subsequent dimensionality estimation. Critically, we found that all algorithms failed when the intrinsic dimensionality was high (above 20) or when the amount of data used for estimation was low. Based on the challenges we observed, we formulated a pipeline for estimating the dimensionality of experimental neural data.

Highlights

  • Studies that simultaneously record the activity of many neurons have shown that cortical neural activity is highly redundant [1]

  • Our procedure aimed at generating simulated data that reproduces possible states of activity of a neural population, without considering the order in which these states might be visited; in other words, we focused on population statistics as opposed to population dynamics

  • We test several representative algorithms on synthetic datasets for which the intrinsic dimensionality is known, to assess their ability to estimate the true dimensionality of the data across a range of simulated conditions relevant to neuroscience

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Summary

Introduction

Studies that simultaneously record the activity of many neurons have shown that cortical neural activity is highly redundant [1]. In primary motor cortex (M1), redundancy arises as tens of millions of neurons control tens or at most hundreds of muscles. This redundancy implies significant covariation in the activity of many neurons, which confines the population neural activity to a low-dimensional manifold embedded in the neural space of all possible patterns of neural population activity [2,3,4,5,6,7,8,9]. Projecting the observed firing patterns onto the manifold yields a low-dimensional set of latent signals that can simplify the interpretation of population neural activity [2,9,22]. Low-dimensional latent signals can facilitate the manipulation or the extraction of signals for brain-computer interfaces, a rehabilitative technology that converts neural signals into control commands to restore movement to paralyzed patients [23,24]

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