'HJ-Biplot' using Different Ways of Penalization Plotting with 'ggplot2'.

SparseBiplots

Overview

Sparse Biplots are modern variant of HJ-Biplot which attempts to find sparse loadings, i.e., weight vectors with only a few nonzero values. Introducing a penalty parameter helps improve the interpretation of the model because the axis are formed as a linear combination of only some of the original variables.

This package provides functions to perform the HJ-Biplot (Galindo, 1986) and modifications introducing Ridge, LASSO and Elastic Net penalty:

• HJBiplot: performs the HJ-Biplot .
• Ridge_HJBiplot: performs the HJ-Biplot introducing Ridge penalty.
• LASSO_HJBiplot: performs the HJ-Biplot introducing LASSO penalty.
• ElasticNet_HJBiplot: performs the HJ-Biplot introducing Elastic Net penalty. For this use the spca package.
• Plot_Biplot: create the plot of the results obtained with any of the above functions. It generates elegant data visualization using ggplot2 with little code

Installation

• Install SparseBiplots from CRAN:

install.packages("SparseBiplots")

• Install SparseBiplots from GitHub using devtools:

install.packages("devtools")
devtools::install_github("mitzicubillamontilla/SparseBiplots")

Usage

Parameters

• X: data frame which provides the data to be analyzed. All the variables must be numeric.
• Transform.Data: character indicating whether the columns have to be scaled or centered. Allowed values are: "center" and "scale" (default).
• lambda: tuning parameter for each penalty. In Elastic Net it refers to LASSO penalty.
• àlpha: tuning parameter of the Ridge shrinkage (just allowed with Elastic Net penalty).
• operator: operator used to solve the norm L1 (just allowed with LASSO penalty). Allowed values are: 'Hard-Thresholding' and 'Soft-Thresholding'.
• ind_name: logical value which indicates if prints the name for each row of X (FALSE by default).
• vec_name: logical value which indicates if prints the name for each column of X (TRUE by default).

Values

• loadings: loadings matrix.
• coord_ind: row coordinates matrix (individuals).
• coord_var: column coordinates matrix (variables).
• eigenvalues: approximated eigenvalues vector.
• explvar: vector containing the proportion of variance explained by the k axis obtained.
• n_ceros: matrix which indicates the number of loadings equal to cero in each axis (output exclusive just for LASSO and Elastic net penalties)

Plot_Biplot parameters

• X: list containing the output of one of the functions of the package.
• axis: vector with lenght 2 which contains the axis ploted in x and y axis.
• hide: vector specifying the elements to be hidden on the plot. Default value is “none”. Other allowed values are “ind” and “var”.
• labels: it indicates the label for points. If it is "auto" the labels are the row names of the coordinates of individuals. If it isn't auto it would be a vector containing the labels.
• ind.shape: points shapes. It can be a number to indicate the shape of all the points or a factor to indicate different shapes.
• ind.color: points colors. It can be a character indicating the color of all the points or a factor to use different colors.
• ind.size: numeric value indicating the size of points.
• ind.label: logical name indicating if prints the row names.
• ind.label.size: numeric value indicating the size of the label of points.
• var.col: character indicating the color of the arrows.
• var.size: size of arrow.
• var.arrow.type: one of "open" or "closed" indicating whether the arrow head should be a closed triangle.
• var.arrow.angle: the angle of the arrow head in degrees (smaller numbers produce narrower, pointier arrows). Essentially describes the width of the arrow head.
• var.arrow.length: length of the arrow head (in cm).
• var.label: logical name indicating if prints the column names.
• var.label.size: numeric value indicating the size of the labels of variables.
• var.label.angle: logical value indicating if print the vector names with orentation of the angle of the vector.

Example

library("SparseBiplots")
hj.biplot <- HJBiplot(mtcars)

It fit the HJ-Biplot on the R data mtcars returning a list that contains the results of the fiting (hj_mtcars). To create the plot use the function Plot_Biplot over the list obtained.

Plot_Biplot(hj.biplot, ind.label = TRUE)

References

• Cubilla-Montilla, M. I. (2019). Contribuciones al análisis biplot basadas en soluciones factoriales disjuntas y en soluciones sparse (Doctoral dissertation, Universidad de Salamanca).
• Erichson, N. B., et al. (2018). Sparse principal component analysis via variable projection.
• Galindo, M. P. (1986). Una Alternativa de Representación Simultanea: HJ-Biplot. Qüestiió, 10:13-23.