solvebeta: The SPCA solver of beta for the elastic net problem

In ipapercodes/FGSPCA: Feature Grouping and Sparse Principal Component Analysis (FGSPCA)

Description

The beta solver using the sparse PCA.

Usage

solvebeta(
  x,
  y,
  paras,
  max.steps,
  sparse = "penalty",
  eps = .Machine$double.eps
)

Arguments

x	the data matrix X_{n\times p}
y	the response vector Y_{n\times 1}
paras	the combination of parameters (λ_2, λ_1)\ lambda = paras[1] (which is lambda2) and lambda1 = paras[2] .
max.steps	100 (default) the maximum number of steps for the updating
sparse	sparse = c("penalty", "varnum")
eps	the tolerance of the stopping criterion for the termination

Details

The standard objective function of elastic net is

1/(2n) \| Y-Xβ\|_2^2 + λ (α \|β\|_1 + (1-α )/2\|β\|_2^2) .

But here we use the following objective function

1/(2n) \| Y-Xβ\|_2^2 + λ_1 \|β\|_1 + λ_2/2 \|β\|_2^2 .

Value

the solution β in each subproblem

References

• Zou, Hui, Trevor Hastie, and Robert Tibshirani. "Sparse principal component analysis." Journal of computational and graphical statistics 15.2 (2006): 265-286.

ipapercodes/FGSPCA documentation built on Dec. 20, 2021, 7:58 p.m.