LRSPAT: A low-rank framework for spatial omics statistics
- 1Dartmouth College
Abstract
We describe LRSPAT (low-rank spatial toolkit), a fast and memory-efficient framework for approximating measures of spatial association for high-dimensional data. While LRSPAT can be applied to any multivariate spatial dataset, development was motivated by the computational challenge of identifying spatially variable genes in high-resolution spatial transcriptomics (ST) data generated by technologies such as 10x Visium HD, Xenium and Atera. LRSPAT leverages a truncated SVD of the expression data and a thresholded spatial weights matrix to perform reduced-rank reconstruction of spatial statistics in the quadratic form family, including global and local versions of Moran's I, Geary's C, and Getis-Ord G. A regularization approach is leveraged to account for the inflated null distribution of spatial statistics computed on latent variables. By performing key operations on the low-dimensional embeddings, LRSPAT is orders of magnitude faster than standard implementations with significantly lower memory requirements. Because the low-rank approach denoises and desparsifies ST data, LRSPAT is also more accurate than standard techniques at identifying genes with true spatial expression patterns. The dramatic improvements in execution time and memory consumption enable the genome-wide analysis of spatially variable genes (SVGs) and exploration of the full range of hyperparameters including spatial scale, distance metric, and embedding rank. This preprint outlines the background and mathematical details of the approach with limited preliminary results and a short conclusion.
Related
- RKMR: A Rapid Kernel Machine Regression Framework for Optimal Marker Detection in Spatial Omics Data
- Spatial multi-omics reveals novel vascular adipocyte and B cell biology in human abdominal aortic aneurysm
- Integrating multi-omics analysis reveals shared genetic architecture and spatial correlations between heart failure and osteoporosis
- Rank-based integration identifies convergent disease mechanisms across omics
- Scale-resolved correlation functions unify spatial omics across platforms and resolutions
BibTeX
@misc{frost2026lrspat,
title = {{LRSPAT: A low-rank framework for spatial omics statistics}},
author = {H. R. Frost},
howpublished = {bioRxiv},
year = {2026},
month = aug,
doi = {10.64898/2026.08.26.747291},
url = {https://www.biorxiv.org/content/10.64898/2026.08.26.747291v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - LRSPAT: A low-rank framework for spatial omics statistics
AU - H. R. Frost
PY - 2026
DA - 2026/08/26
PB - bioRxiv
DO - 10.64898/2026.08.26.747291
UR - https://www.biorxiv.org/content/10.64898/2026.08.26.747291v1
AB - We describe LRSPAT (low-rank spatial toolkit), a fast and memory-efficient framework for approximating measures of spatial association for high-dimensional data. While LRSPAT can be applied to any multivariate spatial dataset, development was motivated by the computational challenge of identifying spatially variable genes in high-resolution spatial transcriptomics (ST) data generated by technologies such as 10x Visium HD, Xenium and Atera. LRSPAT leverages a truncated SVD of the expression data and a thresholded spatial weights matrix to perform reduced-rank reconstruction of spatial statistics in the quadratic form family, including global and local versions of Moran's I, Geary's C, and Getis-Ord G. A regularization approach is leveraged to account for the inflated null distribution of spatial statistics computed on latent variables. By performing key operations on the low-dimensional embeddings, LRSPAT is orders of magnitude faster than standard implementations with significantly lower memory requirements. Because the low-rank approach denoises and desparsifies ST data, LRSPAT is also more accurate than standard techniques at identifying genes with true spatial expression patterns. The dramatic improvements in execution time and memory consumption enable the genome-wide analysis of spatially variable genes (SVGs) and exploration of the full range of hyperparameters including spatial scale, distance metric, and embedding rank. This preprint outlines the background and mathematical details of the approach with limited preliminary results and a short conclusion.
ER -