linear_PPCA: Probabilistic Principal Component Analysis

In Rdimtools: Dimension Reduction and Estimation Methods

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)

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.

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.

mle.sigma2

MLE for σ^2.

mle.W

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

algorithm

name of the algorithm.

Author(s)

Kisung You

References

\insertRef

tipping_probabilistic_1999Rdimtools

See Also

do.pca

Examples

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

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

## Visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
plot(PCA$Y,  pch=19, col=label, main="PCA")
plot(PPCA$Y, pch=19, col=label, main="PPCA")
par(opar)

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