Ridge_HJBiplot: 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')

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.

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".

Author

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

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).

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.

Examples

Run this code

 Ridge_HJBiplot(mtcars, Lambda = 0.2)

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