2017/02/24 by Tianqi Liu, Ming Yuan, Liu, Tianqi +3 · 21 citations
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Artificial intelligence #Biology #Computational biology #Computer science #Data mining #Expression (computer science) #FOS: Computer and information sciences #Mathematics #Methodology (stat.ME) #Pattern recognition (psychology) #Principal component analysis #Rank (graph theory) #Robust principal component analysis #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #stat.ME
paper · pdf · doi:10.48550/arxiv.1702.07449
published in arXiv (Cornell University) (Cornell University)
arxiv created 2017/02/24 · openalex publication_date 2017/02/24 · arxiv updated 2017/02/27 · openalex created_date 2017/03/16 · openalex updated_date 2026/08/06
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.