High-Dimensional Methods via Generalised Singular Decomposition.

wideRhino

The goal of wideRhino is to enable the construction of canonical variate analysis (CVA) biplots for high-dimensional data settings, specifically where the number of variables ($p$) exceeds the number of observations ($n$). The package addresses the singularity limitation of the within-group scatter matrix by leveraging the generalised singular value decomposition (GSVD).

Installation

You can install the development version of wideRhino from GitHub with:

# install.packages("pak")
pak::pak("RaeesaGaney91/wideRhino")

Example

When $p < n$, then the CVA-GSVD biplot will result to the standard CVA biplot. Here is an example using the penguins data:

library(wideRhino)
Penguins <- datasets::penguins[stats::complete.cases(penguins),]
CVAgsvd(X=Penguins[,3:6],group = Penguins[,1]) |> 
  CVAbiplot(group.col=c("blue","purple","forestgreen"))

When $p > n$, then the standard CVA biplot will not work due to the singularity of the within-scatter matrix, and this is when the GSVD becomes useful. Using a simulated data set with 3 groups, 100 observations and 300 variables, a CVA-GSVD biplot can be constructed:

data(sim_data)
CVAgsvd(X=sim_data[,2:301],group = sim_data[,1]) |>
  CVAbiplot(group.col=c("tan1","darkcyan","darkslateblue"),which.var = 1:10,zoom.out=80)

About the name 🦏

The name wideRhino is inspired by the white rhinoceros, a species distinguished by its wide mouth and short legs. This physical structure reflects the statistical characteristics of the data the package is designed for: wide data with a large number of variables ($p$) and a small number of observations ($n$) — a setting often described as “large $p$, small $n$”.

Just as the white rhino’s wide frame is well-adapted to its environment, wideRhino is purpose-built for the challenges of high-dimensional multivariate analysis. By leveraging the generalised singular value decomposition (GSVD), it allows users to construct canonical variate analysis (CVA) biplots even when classical assumptions break down.