RobRSVD (version 1.0)

RobRSVD: Robust Regularized Singular Value Decomposition

Description

This function provides the Robust Regularized Singular Value Decomposition method based on Zhang, Shen and Huang (2013). We will return the first triplets: singular value, left and right singular vectors, for the first robust and regualrized SVD component.

Usage

RobRSVD(data, irobust = F, huberk = 1.345, iinituv = F, inits, initu, initv, 
niter = 1000, tol = 1e-05, istablize = T, uspar = 0, vspar = 0, iugcv = F, 
ivgcv = F, usparmax = 10000, usparmin = 1e-10, nuspar = 14, iloguspar = T, 
vsparmax = 10000, vsparmin = 1e-10, nvspar = 14, ilogvspar = T)

Value

A list contains the following fieldssThe singular valueuThe left singular vector, or singular columnvThe right singular vector, or singular rowdiagoutA list of diagnosis measures, which include ugcvscore, vgcvscore, ugcvmat and vgcvmat

Details

This program applied alternating regression technique to estimate singular value decomposition. The usual least squares for regular SVD is replaced by the iterative reweighted least squares to achieve robustness.

References

Zhang, L., Shen, H., & Huang, J. Z. (2013). Robust regularized singular value decomposition with application to mortality data. The Annals of Applied Statistics, 7(3), 1540-1561.

See Also

See Also as svd, svd3dplot

Examples

#generate a simulated data set, which is provided in Zhang et al (2013) AoAS paper.
u0<-log(10/9)*10^seq(0, 1, length=100)
v0<-sin(2*pi*seq(0, 1, length=100))/(1+1/pi)
s0<-773
data0<-s0*u0 %*% t(v0)
data<-data0+matrix(rnorm(10000, sd=20), nrow=100)
data[ceiling(10000*runif(50))]<-max(data0)+max(data0)*runif(50)
#the above provides random outlying cell simulation

#the svd calculation
data.svd<-RobRSVD(data, irobust=FALSE, uspar=0, vspar=0)

#the robsvd calculation
data.robsvd<-RobRSVD(data, irobust=TRUE, uspar=0, vspar=0)

#the ssvd calculation
data.ssvd<-RobRSVD(data, irobust=FALSE, iugcv=TRUE, ivgcv=TRUE)

#the robrsvd calculation
data.robrsvd<-RobRSVD(data, irobust=TRUE, iugcv=TRUE, ivgcv=TRUE)

#compare v's
plot(data.svd$v, type='l', ylab='V')
lines(data.robrsvd$v, col=2)
lines(data.ssvd$v, col=6)
lines(data.robsvd$v, col=4)

#compare u's
plot(data.svd$u, type='l', ylab='U')
lines(data.robrsvd$u, col=2)
lines(data.ssvd$u, col=6)
lines(data.robsvd$u, col=4)

#compare approximation matrices
#app.svd=data.svd$s * data.svd$u %*% t(data.svd$v)
#app.ssvd=data.ssvd$s * data.ssvd$u %*% t(data.ssvd$v)
#app.robsvd=data.robsvd$s * data.robsvd$u %*% t(data.robsvd$v)
#app.robrsvd=data.robrsvd$s * data.robrsvd$u %*% t(data.robrsvd$v)

#par(mfrow=c(2, 2))
#persp(app.svd, main='SVD', theta=-45, phi=40, xlab='', ylab='', zlab='')
#persp(app.ssvd, main='Regularized SVD', theta=-45, phi=40, xlab='', ylab='', zlab='');
#persp(app.robsvd, main='Robust SVD', theta=-45, phi=40, xlab='', ylab='', zlab='');
#persp(app.robrsvd, main='RobRSVD', theta=-45, phi=40, xlab='', ylab='', zlab='');
#dev.off()