A Random Matrix Theory Approach to Denoise Single-Cell Data

Luis Aparicio; Mykola Bordyuh; Andrew J Blumberg; Raul Rabadan

doi:10.1016/j.patter.2020.100035

A Random Matrix Theory Approach to Denoise Single-Cell Data

Patterns (N Y). 2020 May 4;1(3):100035. doi: 10.1016/j.patter.2020.100035. eCollection 2020 Jun 12.

Authors

Luis Aparicio^{1

2}, Mykola Bordyuh^{1

2}, Andrew J Blumberg³, Raul Rabadan^{1

2}

Affiliations

¹ Department of Systems Biology, Columbia University, New York NY 10032, USA.
² Department of Biomedical Informatics, Columbia University, New York NY 10032, USA.
³ Department of Mathematics, University of Texas, Austin, TX 78705, USA.

Abstract

Single-cell technologies provide the opportunity to identify new cellular states. However, a major obstacle to the identification of biological signals is noise in single-cell data. In addition, single-cell data are very sparse. We propose a new method based on random matrix theory to analyze and denoise single-cell sequencing data. The method uses the universal distributions predicted by random matrix theory for the eigenvalues and eigenvectors of random covariance/Wishart matrices to distinguish noise from signal. In addition, we explain how sparsity can cause spurious eigenvector localization, falsely identifying meaningful directions in the data. We show that roughly 95% of the information in single-cell data is compatible with the predictions of random matrix theory, about 3% is spurious signal induced by sparsity, and only the last 2% reflects true biological signal. We demonstrate the effectiveness of our approach by comparing with alternative techniques in a variety of examples with marked cell populations.

Keywords: denoising; eigenvector localization; random matrix theory; single cell; sparsity; universality.

Abstract

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