摘要：SummaryPatterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables. One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. When more genes are taken into account, hyperbolic effects become stronger but representation remains low dimensional. The size of the hyperbolic map, which indicates the hierarchical depth of the data, was the largest for human cells, the smallest for mouse embryonic cells, and intermediate in differentiated cells from different mouse organs. We also describe how hyperbolic metric can be incorporated into the t-SNE method to improve visualizations compared with leading methods.Graphical abstractDisplay OmittedHighlights•A method to identify underlying low-dimensional geometry in high-dimensional dataset•Gene expression data exhibit local Euclidean and large-scale hyperbolic geometry•The size of the hyperbolic map is larger in differentiated and brain cells•Taking into account hyperbolic geometry yields improved visualization of dataGenes; Cell Biology; Complex Systems
