RegularizedSCA (version 0.5.4)

sparseSCA: Variable selection with Lasso and Group Lasso with a multi-start procedure.

Description

Variable selection with Lasso and Group Lasso penalties to identify component and distinctive components. This algorithm incorporates a multi-start procedure to deal with the possible existence of local minima.

Usage

sparseSCA(DATA, Jk, R, LASSO, GROUPLASSO, MaxIter, NRSTARTS, method)

Arguments

DATA

A matrix, which contains the concatenated data with the same subjects from multiple blocks.

Jk

A vector containing number of variables in the concatinated data matrix.

R

Number of components (R>=2).

LASSO

A Lasso tuning parameter.

GROUPLASSO

A group Lasso tuning parameter.

MaxIter

The maximum rounds of iterations. It should be a positive integer. The default value is 400.

NRSTARTS

Multi-start procedure: The number of multi-starts. The default value is 20.

method

"datablock" or "component". If method="component", the algorithm treats each component across all blocks independently, and thus sparse Group Lasso is applied per component. If method="datablock", the algorithm applies sparse Group Lasso on the entire concatenated data block altogether. If method is missing, then the "component" method is used.

Value

Pmatrix

The best estimated component loading matrix (i.e., P), if multi-starts >= 2.

Tmatrix

The best estimated component score matrix (i.e., T), if multi-starts >= 2.

Lossvec

A list of vectors containing the loss in each iteration for each multi-start.

References

Friedman, J., Hastie, T., & Tibshirani, R. (2010). A note on the group lasso and a sparse group lasso. arXiv preprint arXiv:1001.0736.

Yuan, M., & Lin, Y. (2006). Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(1), 49-67.

Examples

# NOT RUN {
DATA1 <- matrix(rnorm(50), nrow=5)
DATA2 <- matrix(rnorm(100), nrow=5) 
DATA <- cbind(DATA1, DATA2)
Jk <- c(10, 20) 
R <- 5 
LASSO <- 0.2 
GROUPLASSO <- 0.4 
MaxIter <- 400
results <- sparseSCA(DATA, Jk, R, LASSO, GROUPLASSO, 
                    MaxIter, NRSTARTS = 10, method = "datablock")

results$Pmatrix 
# }