hierBipartite (version 0.0.2)

scca: Sparse canonical covariance analysis

Description

'scca' is used to perform sparse canonical covariance analysis (SCCA)

Usage

scca(X,Y,penalty="HL",lamx=c(1,2,3),lamy=c(1,2,3),nc=1,
tuning="CV.alt",K=5,seed=NULL,center=TRUE,scale=FALSE)

Arguments

X

n-by-p data matrix, where n is the number of subjects and p is the number of variables

Y

n-by-q data matrix, where q is the number of variables

penalty

"HL" is the unbounded penalty proposed by Lee and Oh (2009). "LASSO" (Tibshirani, 1996), "SCAD" (Fan and Li, 2001) and "SOFT" (soft thresholding) are also available as other penalty options. Default is "HL".

lamx

A vector specifying grid points of the tuning parameter for X. Default is (1,2,3).

lamy

A vector specifying grid points of the tuning parameter for Y. Default is (1,2,3).

nc

Number of components (canonical vectors). Default is 1.

tuning

How to find optimal tuning parameters for the sparsity. If tuning="CV.full", then the tuning parameters are selected automatically via K-fold cross-validation by using 2-dim'l grid search. If "CV.alt", then a sequential 1-dim'l search method is applied instead of the 2-dim'l grid search. Default is "CV.alt".

K

Perform K-fold cross-validation.

seed

Seed number for initialization. A random initial point is generated for tuning="CV.alt".

center

The columns of the data matrix are centered to have mean zero. Default is TRUE.

scale

The columns of the data matrix are scaled to have variance 1. Default is FALSE.

Value

• A: p-by-nc matrix, k-th colum of A corresponds to k-th pattern

• B: q-by-nc matrix, k-th colum of B corresponds to k-th pattern (canonical vector) for Y

• U: n-by-nc matrix. k-th column of U corresponds to k-th score associated with k-th pattern for X

• V: n-by-nc matrix. k-th column of V corresponds to k-th score associated with k-th pattern for Y

• lambda: nc-by-2 matrix. k-th row of lambda corresponds to the optimal tuning parameters for k-th pattern pairs

• CR: average cross-validated sample covariance

Details

Sparse CCA uses a random-effect model approach to obtain sparse regression. This model gives unbounded gains for zero loadings at the origin. Various penalty functions can be adapted as well.

References

Lee, W., Lee, D., Lee, Y. and Pawitan, Y. (2011) Sparse Canonical Covariance Analysis for High-throughput Data

Examples

# NOT RUN {
## Example 1
## A very simple simulation example
n<-10; p<-50; q<-20
X = matrix(rnorm(n*p),ncol=p)
Y = matrix(rnorm(n*q),ncol=q)
scca(X,Y)

# }