Multidimensional scaling informed by F-statistic: Visualizing microbiome for inference

Multidimensional scaling (MDS) is a widely used dimensionality reduction
technique in microbial ecology data analysis that captures the
multivariate structure of the data while preserving pairwise distances
between samples. While improvements in MDS have enhanced the ability to
reveal group-specific data patterns, these MDS-based methods require prior
assumptions for inference, limiting their application in general
microbiome analysis. In this study, we introduce a new MDS-based
ordination method, "F-informed MDS," which configures the data
distribution based on the F-statistic, the ratio of dispersion between
groups sharing common and different characteristics. Using semisynthetic
datasets, we demonstrate that the proposed method is robust to
hyperparameter selection while maintaining statistical significance
throughout the ordination process. Various quality metrics for evaluating
dimensionality reduction confirm that F-informed MDS is comparable to
state-of-the-art methods in preserving both local and global data
structures. Its application to a diatom-associated bacterial community
suggests the role of this new method in interpreting the community’s
response to the host. Our approach offers a well-founded refinement of MDS
that aligns with statistical test results, which can be beneficial for
broader multidimensional data analyses in microbiology and ecology. This
new visualization tool can be incorporated into standard microbiome data
analyses.