ppca {pcaMethods} | R Documentation |
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. Thanks a lot!
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.
Requires MASS
It is not recommended to use this function directely but rather to use the pca() wrapper function.
ppca(Matrix, nPcs = 2, center = TRUE, completeObs = TRUE, seed = NA, ...)
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. |
center |
boolean Mean center the data if TRUE |
completeObs |
boolean Return the complete observations if TRUE. This
is the original data with NA values filled with the estimated values. |
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. |
... |
Reserved for future use. Currently no further parameters are used. |
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 what leads to much 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. This should,
however not be necessary with the lowered threshold.
pcaRes |
Standart PCA result object used by all
PCA-based methods of this package. Contains scores, loadings, data mean and
more. See pcaRes for details. |
Wolfram Stacklies
Max Planck Institut fuer Molekulare Pflanzenphysiologie, Potsdam, Germany
wolfram.stacklies@gmail.com
bpca, svdImpute, prcomp, nipalsPca, pca, pcaRes
.
## Load a sample metabolite dataset with 5% missing values (metaboliteData) data(metaboliteData) ## Perform probabilistic PCA using the 3 largest components result <- pca(metaboliteData, method="ppca", nPcs=3, center=TRUE) ## Get the estimated principal axes (loadings) loadings <- result@loadings ## Get the estimated scores scores <- result@scores ## Get the estimated complete observations cObs <- result@completeObs ## Now plot the scores plotPcs(result, type = "scores")