Rdimtools (version 1.1.2)

do.bpca: Bayesian Principal Component Analysis

Description

Bayesian PCA (BPCA) is a further variant of PCA in that it imposes prior and encodes basis selection mechanism. Even though the model is fully Bayesian, do.bpca faithfully follows the original paper by Bishop in that it only returns the mode value of posterior as an estimate, in conjunction with ARD-motivated prior as well as consideration of variance to be estimated. Unlike PPCA, it uses full basis and returns relative weight for each base in that the smaller \(\alpha\) value is, the more likely corresponding column vector of mp.W to be selected as potential basis.

Usage

do.bpca(X, ndim = 2, ...)

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.

mp.itercount

the number of iterations taken for EM algorithm to converge.

mp.sigma2

estimated \(\sigma^2\) value via EM algorithm.

mp.alpha

length-ndim-1 vector of relative weight for each base in mp.W.

mp.W

an \((ndim\times ndim-1)\) matrix from EM update.

algorithm

name of the algorithm.

Arguments

X

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

ndim

an integer-valued target dimension.

...

extra parameters including

maxiter

maximum number of iterations (default: 100).

reltol

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

Author

Kisung You

References

bishop_bayesian_1999Rdimtools

See Also

do.pca, do.ppca

Examples

if (FALSE) {
## use iris dataset
data(iris)
set.seed(100)
subid = sample(1:150,50)
X     = as.matrix(iris[subid,1:4])
lab   = as.factor(iris[subid,5])

## compare BPCA with others
out1  <- do.bpca(X, ndim=2)
out2  <- do.pca(X,  ndim=2)
out3  <- do.lda(X, lab, ndim=2)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=lab, pch=19, cex=0.8, main="Bayesian PCA")
plot(out2$Y, col=lab, pch=19, cex=0.8, main="PCA")
plot(out3$Y, col=lab, pch=19, cex=0.8, main="LDA")
par(opar)
}