pcaMethods (version 1.64.0)

ppca: Probabilistic PCA

Description

Implementation of probabilistic PCA (PPCA). PPCA allows to perform PCA on incomplete data and may be used for missing value estimation. This script was implemented after the Matlab version provided by Jakob Verbeek ( see http://lear.inrialpes.fr/~verbeek/) and the draft ``EM Algorithms for PCA and Sensible PCA'' written by Sam Roweis.

Usage

ppca(Matrix, nPcs = 2, seed = NA, threshold = 1e-05, maxIterations = 1000, ...)

Arguments

Matrix

matrix -- Data containing the variables in columns and observations in rows. The data may contain missing values, denoted as NA.

nPcs

numeric -- Number of components to estimate. The preciseness of the missing value estimation depends on the number of components, which should resemble the internal structure of the data.

seed

numeric Set the seed for the random number generator. PPCA creates fills the initial loading matrix with random numbers chosen from a normal distribution. Thus results may vary slightly. Set the seed for exact reproduction of your results.

threshold

Convergence threshold.

maxIterations

the maximum number of allowed iterations

...

Reserved for future use. Currently no further parameters are used.

Value

Standard PCA result object used by all PCA-based methods of this package. Contains scores, loadings, data mean and more. See pcaRes for details.

Details

Probabilistic PCA combines an EM approach for PCA with a probabilistic model. The EM approach is based on the assumption that the latent variables as well as the noise are normal distributed.

In standard PCA data which is far from the training set but close to the principal subspace may have the same reconstruction error. PPCA defines a likelihood function such that the likelihood for data far from the training set is much lower, even if they are close to the principal subspace. This allows to improve the estimation accuracy.

A method called kEstimate is provided to estimate the optimal number of components via cross validation. In general few components are sufficient for reasonable estimation accuracy. See also the package documentation for further discussion on what kind of data PCA-based missing value estimation is advisable.

Complexity: Runtime is linear in the number of data, number of data dimensions and number of principal components.

Convergence: The threshold indicating convergence was changed from 1e-3 in 1.2.x to 1e-5 in the current version leading to more stable results. For reproducability you can set the seed (parameter seed) of the random number generator. If used for missing value estimation, results may be checked by simply running the algorithm several times with changing seed, if the estimated values show little variance the algorithm converged well.

See Also

bpca, svdImpute, prcomp, nipalsPca, pca, pcaRes.

Examples

## Load a sample metabolite dataset with 5\% missing values (metaboliteData)
data(metaboliteData)
## Perform probabilistic PCA using the 3 largest components
result <- pca(t(metaboliteData), method="ppca", nPcs=3, seed=123)
## Get the estimated complete observations
cObs <- completeObs(result)
## Plot the scores
plotPcs(result, type = "scores")