Fig. 1

Workflow of GraphPCA and synthetic experiments validation. a GraphPCA is a novel graph-constrained, interpretable, and quasi-linear dimension-reduction method tailored for ST data. It begins with input data including gene expression matrix X along with spatial coordinates S of spots. It first constructs a spatial neighborhood graph G using the spatial coordinates S and sets the graph constraint parameter \(\lambda\) to characterize the spatial relationships and dependences in the low-dimensional embedding Z. Subsequently, GraphPCA infers the embedding matrix Z by integrating both spatial location S and gene expression information X by solving a non-convex optimization problem with graph constraints. The output of GraphPCA can be readily utilized for various downstream analysis tasks including spatial domain detection, trajectory inference, and denoising. b In simulation, we obtained the anatomical structure of mouse brain sagittal from the Allen Brain Atlas as ground truth layer labels and simulated ST data using scDesign3. c Clustering accuracies of GraphPCA on simulated datasets across varying values of the graph constraint parameter \(\lambda\) (x-axis). d Clustering accuracies of different methods on simulated data. Error bars indicate 95% confidence intervals across 20 replicates. e The robustness of GraphPCA and other methods under varying simulation scenarios including different sequencing depths, noise levels, spot sparsity, and expression dropout rates. For each scenario and method, dots represent the mean ARI calculated across 20 replicates