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.

翻译：降维技术是高维数据分析中最重要的分析工具之一。广义主成分分析（PCA）是标准PCA的扩展，被广泛用于识别高维离散数据（如二值、多类别和计数数据）中的低维特征。尤其对于微生物组计数数据，多项式PCA是标准PCA的自然对应方法。然而，该技术未能解释微生物组计数数据中常见的过度零值问题。为处理稀疏性，可采用零膨胀多元分布。我们提出了一种用于潜在因子分析的零膨胀概率PCA模型。该模型是一种完全贝叶斯因子分析方法，适用于微生物组计数数据分析。此外，我们利用平均场变分族来近似边际似然，并开发了一种分类变分逼近算法来拟合模型。通过模拟实验，我们展示了基于潜在因子和模型参数进行预测的流程效率，证明了其相对于竞争方法的优越性。这一效率进一步通过两个真实微生物组计数数据集得到验证。该方法已在R语言中实现。