Single-cell RNA-Seq (scRNA-seq) has become an invaluable tool for studying biological systems in health and diseases. While dimensionality reduction is a crucial step in interpreting the relation between cells based on scRNA-seq, current methods often are hampered by "crowding" of cells in the center of the latent space, biased by batch effects, or inadequately capture developmental relationships. Here, we introduced scPhere, a scalable deep generative model to embed cells into low-dimensional hyperspherical or hyperbolic spaces, as a more accurate representation of the data. ScPhere resolves cell crowding, corrects multiple, complex batch factors, facilitates interactive visualization of large datasets, and gracefully uncovers pseudotemporal trajectories. We demonstrate scPhere on six large datasets in complex tissue from human patients or animal development, demonstrating how it controls for both technical and biological factors and highlights complex cellular relations and biological insights.
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