Abstract
In recent years microbiome studies have become increasingly prevalent and large-scale. Through high-throughput sequencing technologies and well-established analytical pipelines, relative abundance data of operational taxonomic units and their associated taxonomic structures are routinely produced. Since such data can be extremely sparse and high dimensional, there is often a genuine need for dimension reduction to facilitate data visualization and downstream statistical analysis. We propose Principal Amalgamation Analysis (PAA), a novel amalgamation-based and taxonomy-guided dimension reduction paradigm for microbiome data. Our approach aims to aggregate the compositions into a smaller number of principal compositions, guided by the available taxonomic structure, by minimizing a properly measured loss of information. The choice of the loss function is flexible and can be based on familiar diversity indices for preserving either within-sample or between-sample diversity in the data. To enable scalable computation, we develop a hierarchical PAA algorithm to trace the entire trajectory of successive simple amalgamations. Visualization tools including dendrogram, scree plot, and ordination plot are developed. The effectiveness of PAA is demonstrated using gut microbiome data from a preterm infant study and an HIV infection study.