  Dimension reduction of high-dimensional microbiome data facilitates
subsequent analysis such as regression and clustering. Most existing reduction
methods cannot fully accommodate the special features of the data such as
count-valued and excessive zero reads. We propose a zero-inflated Poisson
factor analysis (ZIPFA) model in this article. The model assumes that
microbiome absolute abundance data follow zero-inflated Poisson distributions
with library size as offset and Poisson rates negatively related to the
inflated zero occurrences. The latent parameters of the model form a low-rank
matrix consisting of interpretable loadings and low-dimensional scores which
can be used for further analyses. We develop an efficient and robust
expectation-maximization (EM) algorithm for parameter estimation. We
demonstrate the efficacy of the proposed method using comprehensive simulation
studies. The application to the Oral Infections, Glucose Intolerance and
Insulin Resistance Study (ORIGINS) provides valuable insights into the relation
between subgingival microbiome and periodontal disease.
