A Random Matrix Approach to Single Cell RNA-seq Analysis

Single cell RNA-seq (scRNAseq) workflows typically start with a raw expression matrix and end with the clustering of sampled cells. Viewed broadly, scRNAseq is a signal processing workflow that takes a transcriptional signal as input and outputs a cell clustering. Currently, we lack a quantitative framework through which to describe the input signal and assess the dependence of correct clustering on the signal properties. As a result, fundamental questions regarding the resolution of scRNAseq remain unanswered and experimentalists have little guidance in determining whether a hypothesized cell type will be clustered by a particular scRNAseq experiment. In this work, we define the notion of a transcriptional signal associated with a gene module, show that the tools of random matrix theory can be used to characterize the signal as it moves through a common (PCA-based) scRNAseq workflow, and develop estimates for cell clustering based on the signal properties and, in particular, the signal strength. We give a formula - that can be computed from expression data - for the signal strength, providing a framework through which scRNAseq resolution can be investigated.