Poisson PCA for matrix count data

Abstract

We develop a dimension reduction framework for data consisting of matrices of counts. Our model is based on the assumption of existence of a small amount of independent normal latent variables that drive the dependency structure of the observed data, and can be seen as the exact discrete analogue of a contaminated low-rank matrix normal model. We derive estimators for the model parameters and estab-lish their limiting normality. An extension of a recent proposal from the literature is used to estimate the latent dimension of the model. The method is shown to outperform both its vectorization-based com-petitors and matrix methods assuming the continuity of the data distribution in analysing simulated data and real world abundance data.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )