Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition

TL;DR

This paper introduces a low rank tensor decomposition method for analyzing complex spatiotemporal gene expression data in the human brain, capturing heterogeneity and evolution of gene regulation patterns over time.

Contribution

It generalizes PCA to tensor PCA for simultaneous spatial and temporal analysis, with an efficient algorithm and statistical guarantees, applied to brain data.

Findings

Revealed heterogeneity in temporal dynamics across brain regions.

Captured evolving spatial gene expression patterns.

Demonstrated improved analysis over existing methods.

Abstract

Spatiotemporal gene expression data of the human brain offer insights on the spa- tial and temporal patterns of gene regulation during brain development. Most existing methods for analyzing these data consider spatial and temporal profiles separately with the implicit assumption that different brain regions develop in similar trajectories, and that the spatial patterns of gene expression remain similar at different time points. Al- though these analyses may help delineate gene regulation either spatially or temporally, they are not able to characterize heterogeneity in temporal dynamics across different brain regions, or the evolution of spatial patterns of gene regulation over time. In this article, we develop a statistical method based on low rank tensor decomposition to more effectively analyze spatiotemporal gene expression data. We generalize the clas- sical principal component analysis (PCA) which is applicable only to data matrices, to tensor PCA that can simultaneously capture spatial and temporal effects. We also propose an efficient algorithm that combines tensor unfolding and power iteration to estimate the tensor principal components, and provide guarantees on their statistical performances. Numerical experiments are presented to further demonstrate the mer- its of the proposed method. An application of our method to a spatiotemporal brain expression data provides insights on gene regulation patterns in the brain.