Rdimtools (version 1.1.2)

do.spca: Sparse Principal Component Analysis

Description

Sparse PCA (do.spca) is a variant of PCA in that each loading - or, principal component - should be sparse. Instead of using generic optimization package, we opt for formulating a problem as semidefinite relaxation and utilizing ADMM.

Usage

do.spca(X, ndim = 2, mu = 1, rho = 1, ...)

Value

a named Rdimtools S3 object containing

Y

an \((n\times ndim)\) matrix whose rows are embedded observations.

projection

a \((p\times ndim)\) whose columns are basis for projection.

algorithm

name of the algorithm.

Arguments

X

an \((n\times p)\) matrix whose rows are observations and columns represent independent variables.

ndim

an integer-valued target dimension.

mu

an augmented Lagrangian parameter.

rho

a regularization parameter for sparsity.

...

extra parameters including

maxiter

maximum number of iterations (default: 100).

abstol

absolute tolerance stopping criterion (default: 1e-8).

reltol

relative tolerance stopping criterion (default: 1e-4).

Author

Kisung You

References

zou_sparse_2006Rdimtools

daspremont_direct_2007Rdimtools

ma_alternating_2013Rdimtools

See Also

do.pca

Examples

# \donttest{
## use iris data
data(iris, package="Rdimtools")
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
lab   = as.factor(iris[subid,5])

## try different regularization parameters for sparsity
out1 <- do.spca(X,ndim=2,rho=0.01)
out2 <- do.spca(X,ndim=2,rho=1)
out3 <- do.spca(X,ndim=2,rho=100)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=lab, pch=19, main="SPCA::rho=0.01")
plot(out2$Y, col=lab, pch=19, main="SPCA::rho=1")
plot(out3$Y, col=lab, pch=19, main="SPCA::rho=100")
par(opar)
# }