Spatial transcriptomics dimensionality reduction using wavelet bases

Background: Spatially resolved transcriptomics (ST) measures gene expression along with the spatial coordinates of the measurements. The analysis of ST data involves significant computation complexity. In this work, we propose a gene expression dimensionality reduction algorithm that retains spatial structure. Methods: : We combine the wavelet transformation with matrix factorization to select spatially-varying genes. We extract a low-dimensional representation of these genes. We adopt an Empirical Bayes perspective, imposing regularization through the prior distribution of factor genes. Additionally, we visualize the extracted representations, providing an overview of global spatial patterns. We illustrate the performance of our methods through spatial structure recovery and gene expression reconstruction using a simulation and real data analysis. Results: : In real data experiments, our method identifies spatial structure of gene factors and outperforms regular decomposition regarding reconstruction error. We find a connection between the fluctuation of gene patterns and wavelet estimates, and this allows us to provide smoother visualizations. We develop the package and share the workflow generating reproducible quantitative results and gene visualization. The package is available at https://github.com/OliverXUZY/waveST. Conclusions: : We have proposed a pipeline for dimensionality reduction that respects spatial structure. Both simulations and real data experiments demonstrate that wavelet and shrinkage techniques show positive results in spatially resolved transcriptomics data. We highlight the idea of combining image processing techniques and statistical methods for application in a spatial genomics context