  Single-cell RNA-sequencing technologies may provide valuable insights to the
understanding of the composition of different cell types and their functions
within a tissue. Recent technologies such as spatial transcriptomics, enable
the measurement of gene expressions at the single cell level along with the
spatial locations of these cells in the tissue. Dimension-reduction and spatial
clustering are two of the most common exploratory analysis strategies for
spatial transcriptomic data. However, existing dimension reduction methods may
lead to a loss of inherent dependency structure among genes at any spatial
location in the tissue and hence do not provide insights of gene co-expression
pattern. In spatial transcriptomics, the matrix-variate gene expression data,
along with spatial co-ordinates of the single cells, provides information on
both gene expression dependencies and cell spatial dependencies through its row
and column covariances. In this work, we propose a flexible Bayesian approach
to simultaneously estimate the row and column covariances for the
matrix-variate spatial transcriptomic data. The posterior estimates of the row
and column covariances provide data summaries for downstream exploratory
analysis. We illustrate our method with simulations and two analyses of real
data generated from a recent spatial transcriptomic platform. Our work
elucidates gene co-expression networks as well as clear spatial clustering
patterns of the cells.
