Ridge_HJBiplot {SparseBiplots}

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)