A Statistical Approach to Dimensionality Reduction Reveals Scale and Structure in scRNA-seq Data

Abstract

While single-cell "omics" based measurements hold the promise of unparalleled biological insight they remain a challenge to analyze owing to their high-dimensional nature. As a result, Dimensionality Reduction (DR) algorithms are necessary for data visualization and for downstream quantitative analysis. The lack of a principled methodology for separating signal from noise in DR algorithmic outputs has limited the confident application of these methods in unsupervised analyses of single-cell data, greatly hampering researchers ability to make data-driven discoveries. In this work we present an approach to quality assessment, EMBEDR, that works in conjunction with any DR algorithm to distinguish signal from noise in dimensionally-reduced representations of high-dimensional data. We apply EMBEDR to t-SNE- and UMAP-generated representations of published scRNA-seq data, revealing where lower-dimensional representations of the data are faithful renditions of biological signal in the data, and where they are more consistent with noise. EMBEDR produces easily interpreted p-values for each cell in a data set, facilitating the comparison of different DR methods and allowing optimization of their global hyperparameters. Most compellingly, EMBEDR allows for the analysis of single-cell data at a single-cell resolution, allowing DR methods to be used in a cell-wise optimal manner. Applying this technique to real data results in a biologically interpretable view of the data with no user supervision. We demonstrate the utility of EMBEDR in the context of several data sets and DR algorithms, illustrating its robustness and flexibility as well as its potential for making rigorous, quantitative analyses of single-cell omics data. EMBEDR is available as a Python package for immediate use.