Fig. 1. Method schematic of SpatialPCA and simulation results.

a SpatialPCA is a spatially aware dimension reduction method that takes both gene expression Y and location information L as inputs. It models the gene expression matrix Y as a function of latent factors Z through a factor analysis model. Importantly, SpatialPCA builds a kernel matrix $\mathit{\Sigma }$ using the location information L to explicitly model the spatial correlation structure in the latent factors Z across tissue locations. Consequently, the inferred low-dimensional components Z from SpatialPCA contain valuable spatial correlation information and can be paired with various analytic tools already developed in scRNA-seq studies to enable effective and improved downstream analyses for spatial transcriptomics. The examined downstream analyses of spatial transcriptomics include spatial transcriptomics visualization, spatial domain detection, trajectory inference on the tissue, and high-resolution spatial map construction. b In simulation, we obtained cortex tissue from the DLPFC data and manually segmented it into four cortical layers. We specified a distinct cell-type composition for each cortical layer and simulate four scenarios. Then we assigned the simulated cells to the locations of the cortex based on the specified cell-type composition in each layer to create the spatial transcriptomics data. We simulated spatial transcriptomics data both at single-cell resolution (sample size n = 10,000 cells) and spot-level (n = 5077 spots) data. We use adjusted Rand index (ARI) to measure the spatial clustering accuracy at single-cell resolution and spot level (spot diameter is 90 µm). The higher ARI indicates better spatial clustering performance. SpatialPCA outperforms the other methods for detecting the spatial domains in the simulations. In the boxplot, the center line, box limits and whiskers denote the median, upper, and lower quartiles, and 1.5× interquartile range, respectively.