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.
do.bpca(X, ndim = 2, ...)an \((n\times p)\) matrix or data frame whose rows are observations and columns represent independent variables.
an integer-valued target dimension.
extra parameters including
maximum number of iterations (default: 100).
relative tolerance stopping criterion (default: 1e-4).
a named Rdimtools S3 object containing
an \((n\times ndim)\) matrix whose rows are embedded observations.
a \((p\times ndim)\) whose columns are basis for projection.
the number of iterations taken for EM algorithm to converge.
estimated \(\sigma^2\) value via EM algorithm.
length-ndim-1 vector of relative weight for each base in mp.W.
an \((ndim\times ndim-1)\) matrix from EM update.
name of the algorithm.
Bishop C (1999). “Bayesian PCA.” In Advances in Neural Information Processing Systems, volume 11, 382--388.
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)
}