do.spca {Rdimtools}

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, ...)

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).

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.

Author(s)

Kisung You

References

Zou H, Hastie T, Tibshirani R (2006). “Sparse Principal Component Analysis.” Journal of Computational and Graphical Statistics, 15(2), 265–286.

d'Aspremont A, El Ghaoui L, Jordan MI, Lanckriet GRG (2007). “A Direct Formulation for Sparse PCA Using Semidefinite Programming.” SIAM Review, 49(3), 434–448.

Ma S (2013). “Alternating Direction Method of Multipliers for Sparse Principal Component Analysis.” Journal of the Operations Research Society of China, 1(2), 253–274.

See Also

do.pca

Examples

## 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)