svdImpute: SVDimpute algorithm

In hredestig/pcaMethods: A collection of PCA methods

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.

Usage

svdImpute(Matrix, nPcs = 2, threshold = 0.01, maxSteps = 100,
  verbose = interactive(), ...)

Arguments

Matrix	matrix – Pre-processed (centered, scaled) data with 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.
threshold	The iteration stops if the change in the matrix falls below this threshold.
maxSteps	Maximum number of iteration steps.
verbose	Print some output if TRUE.
...	Reserved for parameters used in future version of the algorithm

Details

Missing values are denoted as NA. It is not recommended to use this function directely but rather to use the pca() wrapper function.

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 variable (for Microarray data genes) as observations.

An optimal linear combination is found by regressing the incomplete variable 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.

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.

Note

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

Author(s)

Wolfram Stacklies

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.

Examples

## Load a sample metabolite dataset with 5\% missing values
data(metaboliteData)
## Perform svdImpute using the 3 largest components
result <- pca(metaboliteData, method="svdImpute", nPcs=3, center = TRUE)
## Get the estimated complete observations
cObs <- completeObs(result)
## Now plot the scores
plotPcs(result, type = "scores")

hredestig/pcaMethods documentation built on Sept. 30, 2023, 10:38 a.m.