linear_BPCA: Bayesian Principal Component Analysis

In Rdimtools: Dimension Reduction and Estimation Methods

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 α value is, the more likely corresponding column vector of mp.W to be selected as potential basis.

Usage

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

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).

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 σ^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.

Author(s)

Kisung You

References

\insertRef

bishop_bayesian_1999Rdimtools

See Also

do.pca, do.ppca

Examples

## Not run: 
## 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)

## End(Not run)

Rdimtools documentation built on Dec. 28, 2022, 1:44 a.m.