Poisson PCA for matrix count data

2021/10/27 by Virta, Joni, Artemiou, Andreas
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2110.14420

Abstract

We develop a dimension reduction framework for data consisting of matrices of counts. Our model is based on assuming the 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 for a contaminated low-rank matrix normal model. We derive estimators for the model parameters and establish their root-n consistency. An extension of a recent proposal from the literature is used to estimate the latent dimension of the model. Additionally, a sparsity-accommodating variant of the model is considered. The method is shown to surpass both its vectorization-based competitors and matrix methods assuming the continuity of the data distribution in analysing simulated data and real abundance data.

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