Rdimtools (version 1.0.0)

do.ppca: Probabilistic Principal Component Analysis

Description

Probabilistic PCA (PPCA) is a probabilistic framework to explain the well-known PCA model. Using the conjugacy of normal model, we compute MLE for values explicitly derived in the paper. Note that unlike PCA where loadings are directly used for projection, PPCA uses \(WM^{-1}\) as projection matrix, as it is relevant to the error model. Also, for high-dimensional problem, it is possible that MLE can have negative values if sample covariance given the data is rank-deficient.

Usage

do.ppca(
  X,
  ndim = 2,
  preprocess = c("center", "scale", "cscale", "decorrelate", "whiten")
)

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.

preprocess

an option for preprocessing the data. This supports three methods. Default is "center". See also aux.preprocess for more details.

Value

a named list containing

Y

an \((n\times ndim)\) matrix whose rows are embedded observations.

trfinfo

a list containing information for out-of-sample prediction.

projection

a \((p\times ndim)\) whose columns are principal components.

mle.sigma2

MLE for \(\sigma^2\).

mle.W

MLE of a \((p\times ndim)\) mapping from latent to observation in column major.

References

tipping_probabilistic_1999Rdimtools

See Also

do.pca

Examples

# NOT RUN {
## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
label = as.integer(iris$Species)

## Compare PCA and PPCA
PCA  <- do.pca(X, ndim=2, preprocess="center")
PPCA <- do.ppca(X, ndim=2, preprocess="center")

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(PCA$Y,  col=label, main="PCA")
plot(PPCA$Y, col=label, main="PPCA")
par(opar)
# }
# NOT RUN {
# }