Three-way clustering of multi-tissue multi-individual gene expression data using constrained tensor decomposition

The advent of next generation sequencing methods has led to an increasing availability of large, multi-tissue datasets which contain gene expression measurements across different tissues and individuals. In this setting, variation in expression levels arises due to contributions specific to genes, tissues, individuals, and interactions thereof. Classical clustering methods are illsuited to explore these three-way interactions, and struggle to fully extract the insights into transcriptome complexity and regulation contained in the data. Thus, to exploit the multi-mode structure of the data, new methods are required. To this end, we propose a new method, called MultiCluster, based on constrained tensor decomposition which permits the investigation of transcriptome variation across individuals and tissues simultaneously. Through simulation and application to the GTEx RNA-seq data, we show that our tensor decomposition identifies three-way clusters with higher accuracy, while being 11x faster, than the competing Bayesian method. For several age-, race-, or gender-related genes, the tensor projection approach achieves increased significance over single-tissue analysis by two orders of magnitude. Our analysis finds gene modules consistent with existing knowledge while further detecting novel candidate genes exhibiting either tissue-, individual-, or tissue-by-individual specificity. These identified genes and gene modules offer bases for future study, and the uncovered multi-way specificities provide a finer, more nuanced snapshot of transcriptome variation than previously possible.