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The human microbiome plays an important role in human health and diseasestatus. Next generating sequencing technologies allow for quantifying thecomposition of the human microbiome. Clustering these microbiome data canprovide valuable information by identifying underlying patterns across samples.Recently, Fang and Subedi (2020) proposed a logistic normal multinomial mixturemodel (LNM-MM) for clustering microbiome data. As microbiome data tends to behigh dimensional, here, we develop a family of logistic normal multinomialfactor analyzers (LNM-FA) by incorporating a factor analyzer structure in theLNM-MM. This family of models is more suitable for high-dimensional data as thenumber of parameters in LNM-FA can be greatly reduced by assuming that thenumber of latent factors is small. Parameter estimation is done using acomputationally efficient variant of the alternating expectation conditionalmaximization algorithm that utilizes variational Gaussian approximations. Theproposed method is illustrated using simulated and real datasets.

Logistic Normal Multinomial Factor Analyzers for Clustering Microbiome Data