# Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition

arXiv: https://arxiv.org/abs/1702.07449 · HTML: https://mlsanity.com/paper/1702.07449/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2017.

## Built on by (most cited first, 8 of 8)

- [Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption](https://mlsanity.com/paper/2305.04080/) (2023)
- [On Estimating Rank-One Spiked Tensors in the Presence of Heavy Tailed Errors](https://mlsanity.com/paper/2107.09660/) (2021)
- [Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model](https://mlsanity.com/paper/2207.04600/) (2022)
- [A Random Matrix Approach to Low-Multilinear-Rank Tensor Approximation](https://mlsanity.com/paper/2402.03169/) (2024)
- [Towards Quantum Tensor Decomposition in Biomedical Applications](https://mlsanity.com/paper/2502.13140/) (2025)
- [Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model](https://mlsanity.com/paper/2307.00575/) (2023)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [MFAI: A Scalable Bayesian Matrix Factorization Approach to Leveraging Auxiliary Information](https://mlsanity.com/paper/2303.02566/) (2023)

## Abstract (arXiv)

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.