Sparse reduced-rank regression for exploratory visualization of paired multivariate datasets

Abstract

In genomics, transcriptomics, and related biological fields (collectively known as omics), it is common to work with n << p datasets with the dimensionality much larger than the sample size. In recent years, combinations of experimental techniques began to yield multiple sets of features for the same set of biological replicates. One example is Patch-seq, a method combining single-cell RNA sequencing with electrophysiological recordings from the same cells. Here we present a framework based on sparse reduced-rank regression for obtaining an interpretable visualization of the relationship between the transcriptomic and the electrophysiological data. We use an elastic net regularization penalty that yields sparse solutions and allows for an efficient computational implementation. Using several publicly available Patch-seq datasets, we show that sparse reduced-rank regression outperforms both sparse full-rank regression and non-sparse reduced-rank regression in terms of predictive performance, and can outperform existing methods for sparse partial least squares and sparse canonical correlation analysis in terms of out-of-sample correlations. We introduce a bibiplot visualization in order to display the dominant factors determining the relationship between transcriptomic and electrophysiological properties of neurons. We believe that sparse reduced-rank regression can provide a valuable tool for the exploration and visualization of paired multivariate datasets, including Patch-seq.