Weighted sliced inverse regression for scalable supervised dimensionality reduction of spatial transcriptomics data

With the dramatic take-up of spatially resolved transcriptomics biotechnologies, performing spatially-aware analysis of the resulting data is crucial to maximise advances in biological understanding. Dimensionality reduction is a first step in almost any analysis of spatial transcriptomics data, regardless of whether the data is collected at the single-cell or spot level. While common approaches, such as principal component analysis, aim to identify low-dimensional scores that preserve total variances of gene expression features, such variances do not usually correspond to biologically relevant spatial variation. To this end, we have developed weighted sliced inverse regression (wSIR), a sufficient dimension reduction technique that performs dimensionality reduction and retains as much predictive power of the spatial coordinates as possible. As a linear dimensionality reduction approach, wSIR is applicable to multiple distinct spatial transcriptomic datasets, and is extremely scalable due to the algorithm and our Rcpp implementation, with over 100, 000 cells processed in under 2 minutes on a standard laptop. The feature loadings are interpretable, and new non-spatial data can be projected into the wSIR low-dimensional space for further downstream analyses. We examine wSIRs performance through benchmarking and demonstrate its capability of biological discovery through two case studies in breast cancer and early embryonic development.