linear_SPCA: Sparse Principal Component Analysis

In kisungyou/Rdimtools: Dimension Reduction and Estimation Methods

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

\insertRef

zou_sparse_2006Rdimtools

\insertRef

daspremont_direct_2007Rdimtools

\insertRef

ma_alternating_2013Rdimtools

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)

kisungyou/Rdimtools documentation built on Jan. 2, 2023, 9:55 a.m.