filling (version 0.2.4)

fill.SVDimpute: Iterative Regression against Right Singular Vectors

Description

Singular Value Decomposition (SVD) is the best low-rank approximation of a given matrix. fill.SVDimpute exploits such idea. First, it starts with simple filling using column mean values for filling. Second, it finds SVD of a current matrix. Then, each row vector is regressed upon top-\(k\) right singular vectors. Missing entries are then filled with predicted estimates.

Usage

fill.SVDimpute(A, k = ceiling(ncol(A)/2), maxiter = 100, tol = 0.01)

Value

a named list containing

X

an \((n\times p)\) matrix after completion.

Arguments

A

an \((n\times p)\) partially observed matrix.

k

the number of regressors to be used.

maxiter

maximum number of iterations to be performed.

tol

stopping criterion for an incremental progress.

References

troyanskaya_missing_2001filling

See Also

fill.KNNimpute

Examples

if (FALSE) {
## load image data of 'lena128'
data(lena128)

## transform 5% of entries into missing
set.seed(5)
A <- aux.rndmissing(lena128, x=0.05)

## apply the method with 3 different number of regressors
fill1 <- fill.SVDimpute(A, k=5)
fill2 <- fill.SVDimpute(A, k=25)
fill3 <- fill.SVDimpute(A, k=50)

## visualize only the last ones from each run
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(A, col=gray((0:100)/100), axes=FALSE, main="5% missing")
image(fill1$X, col=gray((0:100)/100), axes=FALSE, main="5 regressors")
image(fill2$X, col=gray((0:100)/100), axes=FALSE, main="25 regressors")
image(fill3$X, col=gray((0:100)/100), axes=FALSE, main="50 regressors")
par(opar)
}