A major challenge in studying single-cell systems and their underlying biological phenomena is their inherently noisy nature. This noise can be caused by technical artifacts, but also can be of biological origin, such as from the stochasticity of gene expression. Interestingly, single-cell RNA-seq data can be mathematically modeled according to a threefold structure: a random matrix, a sparsity induced signal, and a biological signal. Leveraging on the universality properties of spectral distributions and the localization properties of eigenvectors in Random Matrix Theory, it is possible to extract the biological signal and remove the noise and the sparsity induced signal.
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