svdImpute {pcaMethods}R Documentation

SVDimpute algorithm

Description

This implements the SVDimpute algorithm as proposed by Troyanskaya et al, 2001. The idea behind the algorithm is to estimate the missing values as a linear combination of the k most significant eigengenes.

Missing values are denoted as NA

Usage

svdImpute(Matrix, nPcs = 2, center=TRUE, completeObs=TRUE, threshold = 0.01, 
  maxSteps = 100, 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 the number of components, which should resemble the internal structure of the data.
center Mean center the data if TRUE
completeObs Return the estimated complete observations if TRUE. This is the input data with NA values replaced by the estimated values.
threshold The iteration stops if the change in the matrix falls below this threshold, the default is 0.01. (0.01 was empirically determined by Troyanskaya et. al)
maxSteps Maximum number of iteration steps. Default is 100.
verbose Print some output if TRUE. Default is interactive()
... Reserved for parameters used in future version of the algorithm

Details

As SVD can only be performed on complete matrices, all missing values are initially replaced by 0 (what is in fact the mean on centred data). The algorithm works iteratively until the change in the estimated solution falls below a certain threshold. Each step the eigengenes of the current estimate are calculated and used to determine a new estimate. Eigengenes denote the loadings if pca is performed considering genes as observations.

An optimal linear combination is found by regressing the incomplete gene against the k most significant eigengenes. If the value at position j is missing, the j^th value of the eigengenes is not used when determining the regression coefficients.

Complexity: Each iteration, standard PCA (prcomp) needs to be done for each incomplete gene to get the eigengenes. This is usually fast for small data sets, but complexity may rise if the data sets become very large.

Value

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.

Author(s)

Wolfram Stacklies
Max Planck Institut fuer Molekulare Pflanzenphysiologie, Potsdam, Germany
wolfram.stacklies@gmail.com

References

Troyanskaya O. and Cantor M. and Sherlock G. and Brown P. and Hastie T. and Tibshirani R. and Botstein D. and Altman RB. - Missing value estimation methods for DNA microarrays. Bioinformatics. 2001 Jun;17(6):520-5.

See Also

bpca, ppca, prcomp, nipalsPca, pca, pcaRes.

Examples

## Load a sample metabolite dataset (metaboliteData)
data(metaboliteData)

# Now remove 10% of the data
rows <- nrow(metaboliteData)
cols <- ncol(metaboliteData)
cond<-matrix(runif(rows * cols),rows,cols) < 0.1
metaboliteData[cond] <- NA

## Perform probabilistic PCA using the 3 largest components
result <- pca(metaboliteData, method="svdImpute", 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, scoresLoadings=c(TRUE,FALSE))


[Package pcaMethods version 1.2.3 Index]