fill.SoftImpute {filling}

SoftImpute : Spectral Regularization

Description

fill.SoftImpute implements convex relaxation techniques to generate a sequence of regularized low-rank solutions for matrix completion problems. For the nuclear norm optimization problem, it uses soft thresholding technique iteratively in that the algorithm returns several matrices in accordance with the provided vector of regularization parameters \lambda (lambdas).

Usage

fill.SoftImpute(A, lambdas = c(10, 1, 0.1), maxiter = 100, tol = 0.001)

Arguments

A

an (n\times p) partially observed matrix.

lambdas

a length-t vector regularization parameters.

maxiter

maximum number of iterations to be performed.

tol

stopping criterion for an incremental progress.

Value

a named list containing

X

an (n\times p\times t) cubic array after completion at each lambda value.

References

Mazumder R, Hastie T, Tibshirani R (2010). “Spectral Regularization Algorithms for Learning Large Incomplete Matrices.” J. Mach. Learn. Res., 11, 2287–2322. ISSN 1532-4435.

See Also

fill.HardImpute

Examples

## load image data of 'lena128'
data(lena128)

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

## apply the method with 3 lambda values
fill <- fill.SoftImpute(A, lambdas=c(500,100,50))

## visualize
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(fill$X[,,1], col=gray((0:100)/100), axes=FALSE, main="lambda=500")
image(fill$X[,,2], col=gray((0:100)/100), axes=FALSE, main="lambda=100")
image(fill$X[,,3], col=gray((0:100)/100), axes=FALSE, main="lambda=50")
par(opar)