Probabilistic Count Matrix Factorization for Single Cell Expression Data Analysis

TL;DR

This paper introduces a probabilistic count matrix factorization method tailored for single-cell RNA sequencing data, effectively capturing data variability and enabling improved visualization and clustering compared to traditional PCA and other methods.

Contribution

It proposes a novel sparse Gamma-Poisson factor model with a variational EM inference, specifically designed to handle over-dispersed count data with dropouts in single-cell analysis.

Findings

Outperforms PCA and t-SNE in representing single-cell data.

Provides a low-dimensional embedding suitable for clustering.

Demonstrates effectiveness on publicly available datasets.

Abstract

The development of high throughput single-cell sequencing technologies now allows the investigation of the population level diversity of cellular transcriptomes. This diversity has shown two faces. First, the expression dynamics (gene to gene variability) can be quantified more accurately, thanks to the measurement of lowly-expressed genes. Second, the cell-to-cell variability is high, with a low proportion of cells expressing the same gene at the same time/level. Those emerging patterns appear to be very challenging from the statistical point of view, especially to represent and to provide a summarized view of single-cell expression data. PCA is one of the most powerful framework to provide a suitable representation of high dimensional datasets, by searching for latent directions catching the most variability in the data. Unfortunately, classical PCA is based on Euclidean distances and projections that work poorly in presence of over-dispersed counts that show drop-out events (zero-inflation) 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 data. We especially focus on publicly available single-cell RNA-seq datasets.