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We develop a dimension reduction framework for data consisting of matrices ofcounts. Our model is based on assuming the existence of a small amount ofindependent normal latent variables that drive the dependency structure of theobserved data, and can be seen as the exact discrete analogue for acontaminated low-rank matrix normal model. We derive estimators for the modelparameters and establish their root-$n$ consistency. An extension of a recentproposal from the literature is used to estimate the latent dimension of themodel. Additionally, a sparsity-accommodating variant of the model isconsidered. The method is shown to surpass both its vectorization-basedcompetitors and matrix methods assuming the continuity of the data distributionin analysing simulated data and real abundance data.

Poisson PCA for matrix count data