PenaltyFun: The penalty function consisting of three parts.

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

Description

The penalty function consisting of three parts.

Usage

PenaltyFun(
  beta,
  tau_S,
  lambda1,
  lambda2,
  lambda3,
  nnConstraint = FALSE,
  sparseTruncated = TRUE
)

Arguments

beta	β, the estimation of β
tau_S	τ a global τ, which is assigned to τ_1=τ_2=τ .
lambda1	λ_1, the tuning parameter corresponding to p_1(\cdot)
lambda2	λ_2, the tuning parameter corresponding to p_2(\cdot)
lambda3	λ_3, the tuning parameter corresponding to p_3(\cdot)
nnConstraint	Boolean, indicating the non-negative constraint is true or false, default FALSE
sparseTruncated	Boolean, indicating whether use the truncated L1 penalty or not for sparsity, default TRUE

Details

The three penalties are as follows,

p_1(β) = ∑_{j=1}^p \min\{\frac{|β_j|}{τ_1}, 1\} ,

p_2(β) = ∑_{j < j', (j, j') \in E} \min\{\frac{|β_j - β_{j'}|}{τ_2}, 1\},

p_3(β) = ∑_{j=1}^p (\min\{β_j, 0\})^2 .

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