  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.
