Dimensionality reduction for zero-inflated single cell gene expression analysis

Single cell RNA-seq data allows insight into normal cellular function and diseases including cancer through the molecular characterisation of cellular state at the single-cell level. Dimensionality reduction of such high-dimensional datasets is essential for visualization and analysis, but single-cell RNA-seq data is challenging for classical dimensionality reduction methods because of the prevalence of dropout events leading to zero-inflated data. Here we develop a dimensionality reduction method, (Z)ero (I)nflated (F)actor (A)nalysis (ZIFA), which explicitly models the dropout characteristics, and show that it improves performance on simulated and biological datasets. Text: Single cell RNA expression analysis (scRNA-seq) is revolutionizing whole-organism science allowing the unbiased identification of previously uncharacterized molecular heterogeneity at the cellular level. Statistical analysis of single cell gene expression profiles can highlight putative cellular subtypes, delineating subgroups of T-cells, lung cells and myoblasts. These subgroups can be clinically relevant: for example, individual brain tumors contain cells from multiple types of brain cancers, and greater tumor heterogeneity is associated with worse prognosis. Despite the success of early single cell studies, the statistical tools that have been applied to date are largely generic, rarely taking into account the particular structural features of single cell expression data. In particular, single cell gene expression data contains an abundance of dropout events that lead to zero expression measurements. These dropout events may be the result of technical sampling effects (due to low transcript numbers) or real biology arising from stochastic transcriptional activity (Fig. 1a). Here, we show that the performance of standard dimensionality-reduction algorithms on high-dimensional, single cell expression data can be perturbed by the presence of zero-inflation making them sub-optimal. We present a new dimensionality-reduction model, Zero-Inflated Factor Analysis (ZIFA), that explicitly accounts for the presence of dropouts, and demonstrate that ZIFA outperforms other methods on simulated data and single cell data from recent scRNA-seq studies. The fundamental empirical observation that underlies the zero-inflation model in ZIFA is that the dropout rate for a gene depends on the expected expression level of that gene in the population. Genes with lower expression magnitude are more likely to be affected by dropout than genes that are expressed with greater magnitude. In particular, if the mean level of non-zero expression is given by μ and the dropout rate for that gene by p0, we have found that this dropout relationship can be approximately modelled with a parametric form p0 = exp(-λμ), where λ is a fitted parameter, based on a double exponential function. This relationship is consistent with previous investigations and holds in many existing single cell datasets (Fig. 1b). The use of this parametric form permits fast, tractable linear algebra computations in ZIFA enabling its use on realistically sized datasets in a multivariate setting. ZIFA adopts a latent variable model based on the Factor Analysis (FA) framework and augments it with an additional zero-inflation modulation layer. Like FA, the data generation process assumes that the peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/019141 doi: bioRxiv preprint first posted online May. 8, 2015;