ElasticNet_HJBiplot {SparseBiplots}

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)