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Bioinformatics. 2019 Mar 13. pii: btz177. doi: 10.1093/bioinformatics/btz177. [Epub ahead of print]

Probabilistic Count Matrix Factorization for Single Cell Expression Data Analysis.

Author information

Univ Lyon, Université Lyon 1, CNRS, LBBE UMR 5558, F-69622 Villeurbanne, France.
Université Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK UMR 5224, F-38000 Grenoble, France.
Université de Montpellier, CNRS, IMAG UMR 5149, F-34090 Montpellier, France.
Univ Lyon, ENS Lyon, Université Lyon 1, CNRS, LBMC UMR 5239, F-69007 Lyon, France.
Department of Cell and Molecular Biology, Karolinska Institutet, Stockholm, Sweden.
Université Grenoble Alpes, CNRS, TIMC-IMAG UMR 5525, F-38041 Grenoble, France.



The development of high throughput single-cell sequencing technologies now allows the investigation of the population diversity of cellular transcriptomes. The expression dynamics (gene-to-gene variability) can be quantified more accurately, thanks to the measurement of lowly-expressed genes. In addition, the cell-to-cell variability is high, with a low proportion of cells expressing the same genes at the same time/level. Those emerging patterns appear to be very challenging from the statistical point of view, especially to represent a summarized view of single-cell expression data. PCA is a most powerful tool for high dimensional data representation, by searching for latent directions catching the most variability in the data. Unfortunately, classical PCA is based on Euclidean distance and projections that poorly work in presence of over-dispersed count data with dropout events like single-cell expression data.


We propose a probabilistic Count Matrix Factorization (pCMF) approach for single-cell expression data analysis, that relies on a sparse Gamma-Poisson factor model. This hierarchical model is inferred using a variational EM algorithm. It is able to jointly build a low dimensional representation of cells and genes. We show how this probabilistic framework induces a geometry that is suitable for single-cell data visualization, and produces a compression of the data that is very powerful for clustering purposes. Our method is competed against other standard representation methods like t-SNE, and we illustrate its performance for the representation of single-cell expression (scRNA-seq) data.


Our work is implemented in the pCMF R-package (


Supplementary data are available at Bioinformatics online.

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