Correspondence analysis for dimension reduction, batch integration, and visualization of single-cell RNA-seq data

Effective dimension reduction is essential for single cell RNA-seq (scRNAseq) analysis. Principal component analysis (PCA) is widely used, but requires continuous, normally-distributed data; therefore, it is often coupled with log-transformation in scRNAseq applications, which can distort the data and obscure meaningful variation. We describe correspondence analysis (CA), a count-based alternative to PCA. CA is based on decomposition of a chi-squared residual matrix, avoiding distortive log-transformation. To address overdispersion and high sparsity in scRNAseq data, we propose five adaptations of CA, which are fast, scalable, and outperform standard CA and glmPCA, to compute cell embeddings with more performant or comparable clustering accuracy in 8 out of 9 datasets. In particular, we find that CA with Freeman-Tukey residuals performs especially well across diverse datasets. Other advantages of the CA framework include visualization of associations between genes and cell populations in a "CA biplot," and extension to multi-table analysis; we introduce corralm for integrative multi-table dimension reduction of scRNAseq data. We implement CA for scRNAseq data in corral, an R/Bioconductor package which interfaces directly with single cell classes in Bioconductor. Switching from PCA to CA is achieved through a simple pipeline substitution and improves dimension reduction of scRNAseq datasets.