Decomposition of a set of distributions in extended exponential family form for distinguishing multiple oligo-dimensional marker expression profiles of single-cell populations and visualizing their dynamics.

Single-cell expression analysis is an effective tool for studying the dynamics of cell population profiles. However, the majority of statistical methods are applied to individual profiles and the methods for comparing multiple profiles simultaneously are limited. In this study, we propose a nonparametric statistical method, called Decomposition into Extended Exponential Family (DEEF), that embeds a set of single-cell expression profiles of several markers into a low-dimensional space and identifies the principal distributions that describe their heterogeneity. We demonstrate that DEEF can appropriately decompose and embed sets of theoretical probability distributions. We then apply DEEF to a cytometry dataset to examine the effects of epidermal growth factor stimulation on an adult human mammary gland. It is shown that DEEF can describe the complex dynamics of cell population profiles using two parameters and visualize them as a trajectory. The two parameters identified the principal patterns of the cell population profile without prior biological assumptions. As a further application, we perform a dimensionality reduction and a time series reconstruction. DEEF can reconstruct the distributions based on the top coordinates, which enables the creation of an artificial dataset based on an actual single-cell expression dataset. Using the coordinate system assigned by DEEF, it is possible to analyze the relationship between the attributes of the distribution sample and the features or shape of the distribution using conventional data mining methods.