Sparse reduced‐rank regression for exploratory visualisation of paired multivariate data

In genomics, transcriptomics, and related biological fields (collectively known as omics), combinations of experimental techniques can 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 (RRR) for obtaining an interpretable visualisation of the relationship between the transcriptomic and the electrophysiological data. We use elastic net regularisation that yields sparse solutions and allows for an efficient computational implementation. Using several Patch‐seq datasets, we show that sparse RRR outperforms both sparse full‐rank regression and non‐sparse RRR, as well as previous sparse RRR approaches, in terms of predictive performance. We introduce a bibiplot visualisation in order to display the dominant factors determining the relationship between transcriptomic and electrophysiological properties of neurons. We believe that sparse RRR can provide a valuable tool for the exploration and visualisation of paired multivariate datasets.