Package 'SparseBiplots'

Title: 'HJ-Biplot' using Different Ways of Penalization Plotting with 'ggplot2'.
Description: 'HJ-Biplot' is a multivariate method that allow represent multivariate data on a subspace of low dimension, in such a way that most of the variability of the information is captured in a few dimensions. This package implements three new techniques and constructs in each case the 'HJ-Biplot', adapting restrictions to reduce weights and / or produce zero weights in the dimensions, based on the regularization theories. It implements three methods of regularization: Ridge, LASSO and Elastic Net.
Authors: Mitzi Isabel Cubilla-Montilla <[email protected]>, Carlos Alfredo Torres-Cubilla <[email protected]>, Purificacion Galindo Villardon <[email protected]> and Ana Belen Nieto-Librero <[email protected]>
Maintainer: Mitzi Isabel Cubilla-Montilla <[email protected]>
License: GPL (>= 3)
Version: 4.0.1
Built: 2024-10-31 16:33:23 UTC
Source: https://github.com/mitzicubillamontilla/sparsebiplots

Help Index

Elastic Net HJ Biplot

Description

This function is a generalization of the Ridge regularization method and the LASSO penalty. Realizes the representation of the SPARSE HJ Biplot through a combination of LASSO and Ridge, on the data matrix. This means that with this function you can eliminate weak variables completely as with the LASSO regularization or contract them to zero as in Ridge.

Usage

ElasticNet_HJBiplot(X, Lambda = 1e-04, Alpha = 1e-04, Transform.Data = 'scale')

Arguments

X

array_like;
A data frame with the information to be analyzed
Lambda

float;
Tuning parameter of the LASSO penalty. Higher values lead to sparser components.
Alpha

float;
Tuning parameter of the Ridge shrinkage
Transform.Data

character;
A value indicating whether the columns of X (variables) should be centered or scaled. Options are: "center" that removes the columns means and "scale" that removes the columns means and divide by its standard deviation. Default is "scale".

Details

Algorithm used to perform automatic selection of variables and continuous contraction simultaneously. With this method, the model obtained is simpler and more interpretable. It is a particularly useful method when the number of variables is much greater than the number of observations.

Value

ElasticNet_HJBiplot returns a list containing the following components:

loadings

array_like;
penalized loadings, the loadings of the sparse principal components.

n_ceros

array_like;
number of loadings equal to cero in each component.

coord_ind

array_like;
matrix with the coordinates of individuals.

coord_var

array_like;
matrix with the coordinates of variables.

eigenvalues

array_like;
vector with the eigenvalues penalized.

explvar

array_like;
an vector containing the proportion of variance explained by the first 1, 2,.,k sparse principal components obtained.

Author(s)

Mitzi Cubilla-Montilla, Carlos Torres-Cubilla, Ana Belen Nieto Librero and Purificacion Galindo Villardon

References

  • Galindo, M. P. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio, 10(1), 13-23.

  • Erichson, N. B., Zheng, P., Manohar, K., Brunton, S. L., Kutz, J. N., & Aravkin, A. Y. (2018). Sparse principal component analysis via variable projection. arXiv preprint arXiv:1804.00341.

  • Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the royal statistical society: series B (statistical methodology), 67(2), 301-320.

See Also

spca, Plot_Biplot

Examples

ElasticNet_HJBiplot(mtcars, Lambda = 0.2, Alpha = 0.1)

HJ Biplot

Description

This function performs the representation of HJ Biplot (Galindo, 1986).

Usage

HJBiplot (X, Transform.Data = 'scale')

Arguments

X

array_like;
A data frame which provides the data to be analyzed. All the variables must be numeric.
Transform.Data

character;
A value indicating whether the columns of X (variables) should be centered or scaled. Options are: "center" that removes the columns means and "scale" that removes the columns means and divide by its standard deviation. Default is "scale".

Details

Algorithm used to construct the HJ Biplot. The Biplot is obtained as result of the configuration of markers for individuals and markers for variables in a reference system defined by the factorial axes resulting from the Decomposition in Singular Values (DVS).

Value

HJBiplot returns a list containing the following components:

eigenvalues

array_like;
vector with the eigenvalues.

explvar

array_like;
an vector containing the proportion of variance explained by the first 1, 2,.,k principal components obtained.

loadings

array_like;
the loadings of the principal components.

coord_ind

array_like;
matrix with the coordinates of individuals.

coord_var

array_like;
matrix with the coordinates of variables.

Author(s)

Mitzi Cubilla-Montilla, Carlos Torres-Cubilla, Ana Belen Nieto Librero and Purificacion Galindo Villardon

References

  • Gabriel, K. R. (1971). The Biplot graphic display of matrices with applications to principal components analysis. Biometrika, 58(3), 453-467.

  • Galindo, M. P. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio, 10(1), 13-23.

See Also

Plot_Biplot

Examples

HJBiplot(mtcars)

LASSO HJ Biplot

Description

This function performs the representation of the SPARSE HJ Biplot applying the LASSO regularization, on the original data matrix, implementing the norm L1.

Usage

LASSO_HJBiplot(X, Lambda, Transform.Data = 'scale', Operator = 'Hard-Thresholding')

Arguments

X

array_like;
A data frame which provides the data to be analyzed. All the variables must be numeric.
Lambda

float;
Tuning parameter for the LASSO penalty
Transform.Data

character;
A value indicating whether the columns of X (variables) should be centered or scaled. Options are: "center" that removes the columns means and "scale" that removes the columns means and divide by its standard deviation. Default is "scale".
Operator

character;
The operator used to solve the norm L1. Allowed values are "Soft-Thresholding" and "Hard-Thresholding".

Details

Algorithm that performs a procedure of contraction and selection of variables. LASSO imposes a penalty that causes the charges of some components to be reduced to zero. By producing zero loadings for some components and not zero for others, the Lasso technique performs selection of variables. As the value of the penalty approaches one, the loadings approach zero.

Value

LASSO_HJBiplot returns a list containing the following components:

loadings

array_like;
penalized loadings, the loadings of the sparse principal components.

n_ceros

array_like;
number of loadings equal to cero in each component.

coord_ind

array_like;
matrix with the coordinates of individuals.

coord_var

array_like;
matrix with the coordinates of variables.

eigenvalues

array_like;
vector with the eigenvalues penalized.

explvar

array_like;
an vector containing the proportion of variance explained by the first 1, 2,.,k sparse principal components obtained.

Author(s)

Mitzi Cubilla-Montilla, Carlos Torres-Cubilla, Ana Belen Nieto Librero and Purificacion Galindo Villardon

References

  • Galindo, M. P. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio, 10(1), 13-23.

  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267-288.

  • Tibshirani, R. (2011). Regression shrinkage and selection via the lasso: a retrospective. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(3), 273-282.

See Also

Plot_Biplot

Examples

LASSO_HJBiplot(mtcars, Lambda = 0.2, Operator = 'Hard-Thresholding')

Plotting Biplot

Description

Plot_Biplot initializes a ggplot2-based visualization of the caracteristics presented in the data analized by the Biplot selected.

Usage

Plot_Biplot(X, axis = c(1,2), hide = "none",
 labels = "auto", ind.shape = 19,
 ind.color = "red", ind.size = 2,
 ind.label = FALSE, ind.label.size = 4,
 var.color = "black", var.size = 0.5,
 var.label = TRUE, var.label.size = 4, var.label.angle = FALSE)

Arguments

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 shape. 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

Size of points.
ind.label

Logical value, if it is TRUE it prints the name for each row of X. If it is FALSE (default) does not print the names.
ind.label.size

Numeric value indicating the size of the labels of points.
var.color

Character indicating the color of the arrows.
var.size

Size of arrow.
var.label

Logical value, if it is TRUE (default) it prints the name for each column of X. If it is FALSE does not print the names.
var.label.size

Numeric value indicating the size of the labels of variables.
var.label.angle

Logical value, if it it TRUE (default) it print the vector names with orentation of the angle of the vector. If it is FALSE the angle of all tags is 0.

Value

Return a ggplot2 object.

Author(s)

Mitzi Cubilla-Montilla, Carlos Torres-Cubilla, Ana Belen Nieto Librero and Purificacion Galindo Villardon

See Also

HJBiplot, Ridge_HJBiplot, ElasticNet_HJBiplot

Examples

hj.biplot <- HJBiplot(mtcars)
Plot_Biplot(hj.biplot, ind.label = TRUE)

Ridge HJ Biplot

Description

This function performs the representation of the HJ Biplot applying the Ridge regularization, on the original data matrix, implementing the norm L2.

Usage

Ridge_HJBiplot (X, Lambda, Transform.Data = 'scale')

Arguments

X

array_like;
A data frame which provides the data to be analyzed. All the variables must be numeric.
Lambda

float;
Tuning parameter for the Ridge penalty
Transform.Data

character;
A value indicating whether the columns of X (variables) should be centered or scaled. Options are: "center" that removes the columns means and "scale" that removes the columns means and divide by its standard deviation. Default is "scale".

Details

Algorithm used to contract the loads of the main components towards zero, but without achieving the nullity of any. If the penalty parameter is less than or equal to 1e-4 the result is like Galindo's HJ Biplot (1986).

Value

Ridge_HJBiplot returns a list containing the following components:

eigenvalues

array_like;
vector with the eigenvalues penalized.

explvar

array_like;
an vector containing the proportion of variance explained by the first 1, 2,.,k sparse principal components obtained.

loadings

array_like;
penalized loadings, the loadings of the sparse principal components.

coord_ind

array_like;
matrix with the coordinates of individuals.

coord_var

array_like;
matrix with the coordinates of variables.

Author(s)

Mitzi Cubilla-Montilla, Carlos Torres-Cubilla, Ana Belen Nieto Librero and Purificacion Galindo Villardon

References

  • Galindo, M. P. (1986). Una alternativa de representacion simultanea: HJ-Biplot. Questiio, 10(1), 13-23.

  • Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

  • Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of computational and graphical statistics, 15(2), 265-286.

See Also

Plot_Biplot

Examples

Ridge_HJBiplot(mtcars, Lambda = 0.2)