The Generalized Matrix Decomposition Biplot and Its Application to Microbiome Data.

Area of Science:

• Microbiome Bioinformatics
• Statistical Data Visualization
• Computational Biology

Background:

• Exploratory analysis of human microbiome data commonly uses dimension-reduced graphical displays based on non-Euclidean distances.
• Principal-coordinate analysis (PCoA) plots, while popular, do not reveal relationships between taxa and sample clustering due to their reliance on eigen-decomposition.
• Traditional biplots are unsuitable for microbiome data as they assume Euclidean distances, failing to incorporate non-Euclidean measures like UniFrac or Bray-Curtis.

Purpose of the Study:

• To propose a novel biplot method, the generalized matrix decomposition biplot (GMD-biplot), that effectively visualizes human microbiome data.
• To address the limitations of PCoA plots by integrating non-Euclidean distances and representing both samples and taxa within a shared coordinate system.
• To provide a robust and computationally efficient approach for graphical visualization in microbiome research.

Main Methods:

• Developed the generalized matrix decomposition biplot (GMD-biplot), an extension of singular value decomposition (SVD).
• The GMD-biplot incorporates an arbitrary matrix of similarities (e.g., non-Euclidean distances) and the original taxon abundance matrix.
• Applied the GMD-biplot to analyze multiple real and simulated microbiome datasets.

Main Results:

• The GMD-biplot demonstrated improved clustering capabilities compared to traditional methods.
• It provides a more meaningful representation of the relationship between microbial taxa (variables) and sample groupings.
• The method successfully visualizes both samples and taxa within the same coordinate system, facilitating interpretation.

Conclusions:

• The GMD-biplot offers a powerful and versatile tool for the exploratory analysis of human microbiome data.
• It effectively handles non-Euclidean distances, making it highly suitable for microbial community dissimilarity measures.
• This novel approach enhances the visualization of complex microbiome data, aiding in the identification of key taxa and community structures, and potentially allowing for future sample configuration.