  Single-cell sequencing technologies have significantly advanced molecular and
cellular biology, offering unprecedented insights into cellular heterogeneity
by allowing for the measurement of gene expression at an individual cell level.
However, the analysis of such data is challenged by the prevalence of low
counts due to dropout events and the skewed nature of the data distribution,
which conventional Gaussian factor models struggle to handle effectively. To
address these challenges, we propose a novel Bayesian segmented Gaussian copula
model to explicitly account for inflation of zero and near-zero counts, and to
address the high skewness in the data. By employing a Dirichlet-Laplace prior
for each column of the factor loadings matrix, we shrink the loadings of
unnecessary factors towards zero, which leads to a simple approach to
automatically determine the number of latent factors, and resolve the
identifiability issue inherent in factor models due to the rotational
invariance of the factor loadings matrix. Through simulation studies, we
demonstrate the superior performance of our method over existing approaches in
conducting factor analysis on data exhibiting the characteristics of
single-cell data, such as excessive low counts and high skewness. Furthermore,
we apply the proposed method to a real single-cell RNA-sequencing dataset from
a lymphoblastoid cell line, successfully identifying biologically meaningful
latent factors and detecting previously uncharacterized cell subtypes.
