R package glmnet can be used for constructing a RLR model.

to call this function is shown below,

glmnet(x,y,alpha=0,lambda)

e 4.19 shows how the regression coefficients evolve with the ߣ

an iterated parameter shrinkage process when RLR was applied

ve oil content data. The regression coefficients were obtained by

e glmnet function with the optimal ߣ value as one of the inputs.

4.19, it can be seen that the regression coefficients became more

e divergent during the learning process. When a subset of

n coefficients increased, the other set of regression coefficients

ed to decrease. Finally, the fruit weight became an outstandingly

t variable with the largest regression coefficient. The model fitted

a very well. The R-square of the model was 0.64. The F-statistic

f the model was 5.983e−7.

(a) (b)

The RLR model constructed for the olive oil content data. (a) The evolution of

on coefficients along with the learning cycle. (b) The fitness measurements.

e Lasso linear regression algorithm

on to RLR as a constrained linear regression algorithm, Lasso is

one. RLR employs the L2 constraint, i.e., the sum of squared

rs is constrained to a constant. This ensures the shrinkage of a

the regression coefficients of the less important when a subset of

ssion coefficients of the important variables is increased. Lasso

r the least angle regression [Efron, et al., 2004]. It is a shrinkage