GMD-biplot for microbiome data
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## How to install?

devtools::install_github("taryue/GMDecomp")

• This R package implements the Generalized Matrix Decomposition (GMD), and provides visualization tools, i.e., the screeplot and biplot, of the GMD output.
• Available on GitHub. A vignette on how to use package is also avaialble here.
• Credit to Yue Wang.

## Why should someone use GMDecomp?

• GMDecomp is developed for visualizing biological data whose distances are non-Euclidean, such as the microbiome data.
• It allows the use of general dissimilarity matrices among samples, and displays both the samples and taxa with respect to the same coordinate system.

## How does it compare to other existing biplots?

• Traditional biplots are based on the singular value decomposition of the data matrix (referred to as the SVD-biplot), and require Euclidean distances between samples. They are not appropriate for microbiome data, where non-Euclidean distances are used to characterize dissimilarities among microbial communities.
• In Ecology, the principal coordinate analysis (PCoA) is often used for dimension reduction and exploratory analysis. However, the PCoA plot does not reveal which taxa are related to the observed sample clustering because the configuration of samples is not based on a coordinate system in which both the samples and variables can be represented.
• The GMD-biplot is based on an extension of the SVD, called the generalized matrix decomposition (GMD), which involves an arbitrary matrix of similarities and the original matrix of variable measures, such as taxon abundances. As in a traditional biplot, points represent the samples and arrows represent the variables.
• The GMD-biplot provides a robust and computationally efficient approach for graphical visualization of non-Euclidean data. In addition, the GMD-biplot displays both the samples and taxa with respect to the same coordinate system, which further allows the configuration of future samples.