Exploratory analysis is an important first step for discovering latent structure and generating hypotheses in large biological data sets. However, when the number of variables is large compared to the number of samples, standard methods such as principal components analysis give results that are unstable and difficult to interpret.
Here, we present adaptive generalized principal components analysis (adaptive gPCA), a new method that solves these problems by incorporating information about the relationships among the variables. Adaptive gPCA gives a low-dimensional representation of the samples with axes that are interpretable in terms of groups of closely related variables. We show that adaptive gPCA does well at reconstructing true latent structure in simulated data and demonstrate its use on a study of the effect of antibiotics on the human gut microbiota.
"Adaptive gPCA: A method for structured dimensionality reduction with applications to microbiome data." Ann. Appl. Stat. 13 (2) 1043 - 1067, June 2019. https://doi.org/10.1214/18-AOAS1227