Estimating the dimensionality of the manifold underlying multi-electrode neural recordings

It is generally accepted that the number of neurons in a given brain area far exceeds the information that area encodes. 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 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 from the low-dimensional manifold to 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 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 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. Author Summary The number of neurons that we can record from has increased exponentially for decades; today we can simultaneously record from thousands of neurons. However, the individual firing rates are highly redundant. One approach to identifying important features from redundant data is to estimate the dimensionality of the neural recordings, which represents the number of degrees of freedom required to describe the data without significant information loss. Better understanding of dimensionality may also uncover the mechanisms of computation within a neural circuit. Circuits carrying out complex computations might be higher-dimensional than those carrying out simpler computations. Typically, studies have quantified neural dimensionality using one of several available methods despite a lack of consensus on which method would be most appropriate for neural data. In this work, we used several methods to investigate the accuracy of simulated neural data with properties mimicking those of actual neural recordings. Based on these results, we devised an analysis pipeline to estimate the dimensionality of neural recordings. Our work will allow scientists to extract informative features from a large number of highly redundant neurons, as well as quantify the complexity of information encoded by these neurons.