Poisson PCA for matrix count data

• Published in: Pattern recognition Vol. 138; p. 109401
• Main Authors: Virta, Joni, Artemiou, Andreas
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2023
• Subjects: Discrete data; Kronecker model; Matrix normal distribution; Poisson log-normal distribution; Secondary 62F12; Discrete data; Matrix normal distribution; Kronecker model; Primary 62H12; Poisson log-normal distribution
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2023.109401

•An interpretable latent variable model for count matrix data is obtained through the Kronecker approach.•Estimators for the model parameters are developed and thoroughly studied and, using them, predictions for the latent variables are obtained.•An estimator for the latent dimensionality is proposed.•The method is illustrated and compared to existing methodology with several data examples. 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 establish 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 competitors and matrix methods assuming the continuity of the data distribution in analysing simulated data and real world abundance data.