Title:	Construct Reactive Calibrated Axes Biplots
Version:	1.0.2
Description:	A modern view on the principal component analysis biplot with calibrated axes. Create principal component analysis biplots rendered in HTML with significant reactivity embedded within the plot. Furthermore, the traditional biplot view is enhanced by translated axes with inter-class kernel densities superimposed. For more information on biplots, see Gower, J.C., Lubbe, S. and le Roux, N.J. (2011, ISBN: 978-0-470-01255-0).
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.2.3
Imports:	cluster, crayon (≥ 1.5.2), htmlwidgets (≥ 1.6.2), knitr (≥ 1.43), methods, plotly (≥ 4.10.2)
Depends:	R (≥ 2.10)
NeedsCompilation:	no
Packaged:	2023-11-02 08:20:45 UTC; user-pc
Author:	Ruan Buys [aut, cre, cph], Carel van der Merwe [aut, ths]
Maintainer:	Ruan Buys <ruanbuys8@gmail.com>
Repository:	CRAN
Date/Publication:	2023-11-02 15:50:05 UTC

Determine various measures of fit for the PCA biplot

Description

Print various measures of fit of the biplot display to the console

Usage

FMbiplot(x)

Arguments

Value

A list returned invisibly containing the following fit measures:

• Cumulative Predictivity

• Marginal Predictivity for the first three principal components

• Marginal Adequacy for the first three principal components

• Overall quality of display

Examples

x<-PCAbiplot(iris[,-5])
FMbiplot(x)

Construct a rank-2 PCA biplot

Description

Rank-2 PCA biplots are constructed based on a combination of the first three principal components.

Usage

PCAbiplot(
  x,
  group = NULL,
  scale = TRUE,
  basis = 1:2,
  symbol = "circle",
  color = NULL,
  build_plot = TRUE
)

Arguments

Details

The method performs Principal Component Analysis (PCA) on the input data and constructs both a traditional biplot using vector representation and with calibrated axes. The data is clustered together on the display by the group parameter. The scale parameter determines if SVD is performed on the covariance matrix or correlation of x. It is highly recommended to set scale=TRUE as the rendered display is sensitive to the scaling in x.

By default three sets of principal components are used for the scaffolding axes, namely: 1 and 2, 1 and 3, and 2 and 3. The function constructs these biplots 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. See FMbiplot for the coordinates.

• A button that changes the display from vector representation of the variables, to calibrated axes in their original scale. The vector representation includes a unit circle around the origin.

• Prediction lines are inserted onto the display if an observation is clicked. The prediction lines can be removed by clicking on the legend entry.

Value

A named list of class bipl5 with the following attributes

See Also

print.bipl5 to display the biplot graph and further see TDAbiplot to draw a biplot with calibrated density axes. Fit measures can be obtained by FMbiplot

Examples

## Consruct a biplot with
x<-PCAbiplot(iris[,1:4],group=iris[,5])
#alternatively
print(x)

## Construct a biplot that preserves the correlation structure among the variables
y<-PCAbiplot(iris[,-5],group=iris[,5],scale=TRUE)

Retrieve all valid plotting symbols for plotly library

Description

Retrieve all valid plotting symbols for plotly library

Usage

Symbol_List()

Value

A vector of all the valid plotting symbols used in the plot_ly library.

Examples

Symbol_List()

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 class 'bipl5'
TDAbiplot(
  x,
  dist = NULL,
  inflate = 1,
  alpha = 0.95,
  alpha_Elip = NULL,
  swop = FALSE,
  density.args = NULL,
  color = NULL,
  symbol = "circle"
)

Arguments

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.

Value

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

See Also

PCAbiplot FMbiplot

Examples

## 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)

bipl5: Constructing Reactive Calibrated Axes Biplots

Description

A modern view on PCA biplot with calibrated axes. Create PCA biplots rendered in HTML with significant reactivity embedded on the plot. Furthermore, the traditional biplot view is enhanced by translated axes with interclass kernel densities superimposed.

Details

Author(s)

• Ruan Buys (Maintainer)

• Carel van der Merwe

Core Functions

• PCAbiplot

• TDAbiplot

• FMbiplot

• predict.bipl5

• print.bipl5

Code Availability

The newest version of the package can be obtained on GitHub: https://github.com/RuanBuys/bipl5

bpl5 default color scales

Description

bpl5 default color scales

Usage

colorpal(number = 16)

Arguments

Value

A vector of colors

Examples

colorpal()

Plot an object of class bipl5

Description

Plot an object of class bipl5

Usage

## S3 method for class 'bipl5'
plot(x, y = NULL, ...)

Arguments

Value

A plot_ly graph containing the biplot

Examples

x<-PCAbiplot(iris[,-5])
plot(x)

Method to obtain the predicted or fitted values of the biplot

Description

Extract the fitted values of the biplot display

Usage

## S3 method for class 'bipl5'
predict(object, ...)

Arguments

Value

The function invisibly returns the predicted values of the biplot display, and outputs the predicted values via the kable function

Examples

kable.args<-list()
kable.args$format<-"pipe"
x<-PCAbiplot(iris[,-5])
predict(x,kable.args)

Default print method for an object of class bipl5

Description

Default print method for an object of class bipl5

Usage

## S3 method for class 'bipl5'
print(x, ...)

Arguments

Value

The object is returned invisibly

Examples

x<-PCAbiplot(iris[,1:4],group=iris[,5])
print.bipl5(x)