nlpca {pcaMethods}R Documentation

Non-linear PCA

Description

Neural network based non-linear PCA

Usage

nlpca(Matrix, nPcs=2, center=TRUE, completeObs=TRUE, maxSteps=2*prod(dim(Matrix)), unitsPerLayer=NULL, functionsPerLayer=NULL, weightDecay=0.001, weights=NULL, verbose=interactive(), ...)

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 thenumber 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.
maxSteps numeric – Number of estimation steps. Default is based on a generous rule of thumb.
unitsPerLayer The network units, example: c(2,4,6) for two input units 2feature units (principal components), one hidden layer fornon-linearity and three output units (original amount ofvariables).
functionsPerLayer The function to apply at each layer eg. c("linr", "tanh", "linr")
weightDecay Value between 0 and 1.
weights Starting weights for the network. Defaults to uniform random values but can be set specifically to make algorithm deterministic.
verbose boolean – nlpca prints the number of steps and warning messages if set to TRUE. Default is interactive().
... Reserved for future use. Not passed on anywhere.

Details

Artificial Neural Network (MLP) for performing non-linear PCA. Non-linear PCA is conceptually similar to classical PCA but theoretically quite different. Instead of simply decomposing our matrix (X) to scores (T) loadings (P) and an error (E) we train a neural network (our loadings) to find a curve through the multidimensional space of X that describes a much variance as possible. Classical ways of interpreting PCA results are thus not applicable to NLPCA since the loadings are hidden in the network. However, the scores of components that lead to low cross-validation errors can still be interpreted via the score plot.

Unfortunately this method depend on slow iterations which currently are implemented in R only making this method extremely slow. Furthermore, the algorithm does not by itself decide when it has converged but simply does 'maxSteps' iterations.

Value

pcaRes Standard PCA result object used by all PCA-basedmethods of this package. Contains scores, loadings, data meanand more. See pcaRes for details.

Author(s)

Based on a matlab script by Matthias Scholz <matthias.scholz[at]uni-greifswald.de> and ported to R by HenningRedestig <redestig[at]mpimp-golm.mpg.de>

References

Matthias Scholz, Fatma Kaplan, Charles L Guy, Joachim Kopkaand Joachim Selbig. Non-linear PCA: a missing dataapproach. Bioinformatics, 21(20):3887-3895, Oct 2005

Examples

# Data set with three variables where data points constitute a helix
data(helix)
helixNA <- helix
helixNA <- t(apply(helix, 1, function(x) { x[sample(1:3, 1)] <- NA; x})) # not a single complete observation
helixNlPca <- pca(helixNA, nPcs=1, method="nlpca", maxSteps=1000)
fittedData <- fitted(helixNlPca, helixNA)
plot(fittedData[which(is.na(helixNA))], helix[which(is.na(helixNA))])
# compared to solution by Nipals PCA that cannot extract non-linear patterns
helixNipPca <- pca(helixNA, nPcs=2, method="nipals")
fittedData <- fitted(helixNipPca)
plot(fittedData[which(is.na(helixNA))], helix[which(is.na(helixNA))])

[Package pcaMethods version 1.14.0 Index]