Multidimensional scaling informed by $F$-statistic: Visualizing grouped microbiome data with inference

TL;DR

This paper introduces an $F$-statistic informed multidimensional scaling method for microbiome data visualization, which is robust, statistically sound, and comparable to existing techniques in preserving data structure.

Contribution

The study presents a novel MDS-based ordination method that integrates $F$-statistics for improved, assumption-free visualization of microbiome data.

Findings

Robustness to hyperparameter selection

Maintains statistical significance in ordination

Comparable to state-of-the-art methods in data structure preservation

Abstract

Multidimensional scaling (MDS) is a dimensionality reduction technique for microbial ecology data analysis that represents the multivariate structure while preserving pairwise distances between samples. While its improvement has enhanced the ability to reveal data patterns by sample groups, 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, $F$-informed MDS, which configures the data distribution based on the $F$-statistic, the ratio of dispersion between groups sharing common and different characteristics. Using simulated compositional 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 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 compositional data analyses in microbiology and ecology. This new visualization tool can be incorporated into standard microbiome data analyses.