Bayesian sparse principal coordinates analysis with microbiome discoveries

Abstract

Principal coordinates analysis (PCoA) is a widely used tool for visualizing sample relationships from dissimilarity data. However, classical PCoA produces dense loading vectors, making interpretation difficult, especially in ultrahigh-dimensional settings such as microbiome studies, where identifying a small number of relevant features is crucial. In this talk, I introduce a sparse PCoA framework that incorporates regularization to induce sparsity in the loading structure, leading to more interpretable coordinate axes. To further enhance flexibility and uncertainty quantification, I present a Bayesian sparse PCoA approach based on global--local shrinkage priors, specifically the three-parameter beta normal family, which allows for adaptive feature selection. I also discuss theoretical properties of PCoA in high-dimensional regimes and illustrate the advantages of the proposed methods through simulation studies and real microbiome applications, including Hadza microbiome data. The results demonstrate that sparse Bayesian PCoA provides clearer structural insights and improved interpretability compared with classical PCoA.

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