jsPCA: fast, scalable, and interpretable identification of spatial domains and variable genes across multi-slice and multi-sample spatial transcriptomics data.

Motivation: Spatial transcriptomics technologies record genome-wide measurements of gene expression with high spatial resolution. These technologies generate large and high-dimensional datasets requiring efficient automated methods for their analysis. We introduce joint spatial PCA (jsPCA), a novel, fast, scalable and interpretable method for the automatic identification of spatial domains and variable genes in multi-slice and multi-sample spatial transcriptomics data. Results: jsPCA relies on a simple mathematical formulation of a spatial covariance defined as the product of the gene expression covariance with the spatial autocorrelation. The principal components of this spatial covariance yield a biologically meaningful low-dimensional representation. From this representation, spatial domains are derived by simple clustering and spatially variable genes are identified directly from the principal component coefficients. A joint representation of multiple slices and samples without spatial alignment is obtained by computing common principal components via joint diagonalization. By leveraging data sparsity and non-convex manifold optimization, jsPCA leads to computing time in the order of seconds to minutes, substantially outperforming state-of-the-art approaches. We benchmarked jsPCA against 10 state-of-the-art methods on two reference databases. Our approach demonstrated excellent performance, comparable or better than state-of-the-art methods, while being much faster, interpretable, and scalable to very large datasets.