TDAbiplot: Construct PCA biplots with translated calibrated density axes

Description

Construct various rank-2 PCA biplots with translated axes based on a combination of the first three principal components.

Usage

TDAbiplot(
  x,
  dist = NULL,
  inflate = 1,
  alpha = 0.95,
  alpha_Elip = NULL,
  swop = FALSE,
  density.args = NULL,
  color = NULL,
  symbol = "circle"
)
# S3 method for bipl5
TDAbiplot(
  x,
  dist = NULL,
  inflate = 1,
  alpha = 0.95,
  alpha_Elip = NULL,
  swop = FALSE,
  density.args = NULL,
  color = NULL,
  symbol = "circle"
)

Value

A named list of class bipl5, see PCAbiplot, with the following attributes:

x: A data frame which is the original input data
Z: A matrix of n x 2 representing the coordinates of each observation on the biplot
rank: The rank of the approximated data
scale: Whether the data is standardized prior to performing dimension reduction
group: The grouping vector of the data
mu: The vector of column means of the input data
stddev: Vector of column standard deviations if the scale parameter is set to TRUE.
PCA: The singular value decomposition of the covariance/correlation matrix, see svd
plot: The plotly graph displaying the biplot, see plot_ly
Adequacy: The adequacy of each axis displayed for each set of principal components
Predictivity: The predictivity of each axis displayed for each set of principal components

Arguments

x: An object of class bipl5. See PCAbiplot in this regard.
dist: Minimum distance between each axis. Default is roughly 12.5% of the plot diameter
inflate: Density inflation factor
alpha: Argument passes to alpha_Elip
alpha_Elip: A function taking two arguments, Z and alpha. The output of the function should be a two-column matrix of coordinates which will be used to construct an alpha-ellipse. See details below.
swop: Swop the direction which to which each axis is translated
density.args: Arguments to be passed to the density function
color: Colors to be utilized per class group
symbol: Plotting symbol to be used per class group

Details

This function produces a PCA biplot with translated calibrated axes. The function constructs this biplot in the plot_ly graphing library with reactivity embedded on the display. The following features are available on the display:

A dropdown menu to change the principal components used to construct the display. Currently only the first three pairwise are supported.
A button to give fit statistics of the biplot. Once clicked, a table is added to give the adequacy and predictivity of each axis for the display.
A button that inserts a graph depicting the cumulative predictivity of each axis against the dimension of the biplot.
Prediction lines are inserted onto the display if an observation is clicked. The prediction lines can be removed by clicking on the legend entry.

The alpha_Elip argument is used to subset the biplot plotting coordinates (Z) to remove the effect of outliers in the data. A common suggestion is to use an alphabag or on Convex hull peeling algorithm to strip away extreme points. The alpha-ellipse will be constructed around this data, and will impact the lengths of the calibrated axes.

Examples

Run this code

## Simple illustration of a calibrated density axis biplot
x<-PCAbiplot(iris[,-5],group=iris[,5])
TDAbiplot(x,dist=1,inflate=1)

## Change the plotting characters of class-groups:
y<- x |> TDAbiplot(dist=1,inflate=1,symbol=c("circle","diamond","square"))

## Custom kernel densities can be drawn on the axes:
density.args<-list()
density.args$kernel <- "optcosine"
density.args$bw <- "sj"

y<- x |> TDAbiplot(dist=1,inflate=1,density.args=density.args)

## To lessen the effects of outliers, a smaller alpha-ellipse can be
## used to determine axis lengths. Define a function that strips away
## outliers, for example a convex hull peeling algorithm:

HullPeeling <- function(x,alpha) {
  n<-nrow(x)
  propinside<-1
  target<-1-alpha
  x2<-x
  while (propinside>target) {
    hull<-grDevices::chull(x2)
    x2old<-x2
    x2<-x2[-hull,]
    propinside<-nrow(x2)/n
  }
    return(x2[grDevices::chull(x2),])
}

y<- x |> TDAbiplot(dist=1,inflate=1, alpha_Elip=HullPeeling, alpha=0.4)