Uncovering axes of variation among single-cell cancer specimens.

While several tools have been developed to map axes of variation among individual cells, no analogous approaches exist for identifying axes of variation among multicellular biospecimens profiled at single-cell resolution. For this purpose, we developed 'phenotypic earth mover's distance' (PhEMD). PhEMD is a general method for embedding a 'manifold of manifolds', in which each datapoint in the higher-level manifold (of biospecimens) represents a collection of points that span a lower-level manifold (of cells). We apply PhEMD to a newly generated drug-screen dataset and demonstrate that PhEMD uncovers axes of cell subpopulational variation among a large set of perturbation conditions. Moreover, we show that PhEMD can be used to infer the phenotypes of biospecimens not directly profiled. Applied to clinical datasets, PhEMD generates a map of the patient-state space that highlights sources of patient-to-patient variation. PhEMD is scalable, compatible with leading batch-effect correction techniques and generalizable to multiple experimental designs.