  Dimension reduction techniques are among the most essential analytical tools
in the analysis of high-dimensional data. Generalized principal component
analysis (PCA) is an extension to standard PCA that has been widely used to
identify low-dimensional features in high-dimensional discrete data, such as
binary, multi-category and count data. For microbiome count data in particular,
the multinomial PCA is a natural counterpart of the standard PCA. However, this
technique fails to account for the excessive number of zero values, which is
frequently observed in microbiome count data. To allow for sparsity,
zero-inflated multivariate distributions can be used. We propose a
zero-inflated probabilistic PCA model for latent factor analysis. The proposed
model is a fully Bayesian factor analysis technique that is appropriate for
microbiome count data analysis. In addition, we use the mean-field-type
variational family to approximate the marginal likelihood and develop a
classification variational approximation algorithm to fit the model. We
demonstrate the efficiency of our procedure for predictions based on the latent
factors and the model parameters through simulation experiments, showcasing its
superiority over competing methods. This efficiency is further illustrated with
two real microbiome count datasets. The method is implemented in R.
