LASSO_HJBiplot {SparseBiplots}

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')