A novel metric reveals previously unrecognized distortion in dimensionality reduction of scRNA-seq data

Abstract

High-dimensional data are becoming increasingly common in nearly all areas of science. Developing approaches to analyze these data and understand their meaning is a pressing issue. This is particularly true for single-cell RNA-seq (scRNA-seq), a technique that simultaneously measures the expression of tens of thousands of genes in thousands to millions of single cells. The emerging consensus for analysis workflows significantly reduces the dimensionality of the dataset before performing downstream analysis, such as assignment of cell types. One problem with this approach is that dimensionality reduction can introduce substantial distortion into the data; consider the familiar example of trying to represent the three-dimensional earth as a two-dimensional map. It is currently unclear if such distortion affects analysis of scRNA-seq data. Here, we introduce a straightforward approach to quantifying this distortion by comparing the local neighborhoods of points before and after dimensionality reduction. We found that popular techniques like t-SNE and UMAP introduce substantial distortion even for relatively simple simulated data sets. For scRNA-seq data, we found the distortion in local neighborhoods was often greater than 95% in the representations typically used for downstream analyses. This level of distortion can introduce errors into cell type identification, pseudotime ordering, and other analyses. We found that principal component analysis can generate accurate embeddings, but only when using dimensionalities that are much higher than typically used in scRNA-seq analysis. Our work suggests the need for a new generation of dimensional reduction algorithms that can accurately embed high dimensional data in its true latent dimension.