ssvd.iter.thresh: Iterative thresholding sparse SVD
In ssvd: Sparse SVD

Description Usage Arguments Value Author(s) References Examples

The function computes sparse SVD by iterative thresholding algorithm with an initializtion as one of the inputs

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ssvd.iter.thresh(x, method = c("theory", "method"), u.old, v.old, 
gamma.u = sqrt(2), gamma.v = sqrt(2), dothres = "hard", r = ncol(u.old), 
tol = 1e-08, n.iter = 100, n.boot = 100, sigma = NA, non.orth = FALSE)

`x`	Input matrix, for which one would like to get a sparse SVD.
`method`	If method = "theory", then a theoretical procedure is adopted which is based on normal assumption on the noise. If method = "method", then the function bypass the normal assumption by some robust statistics. These two choices typically give similar solutions, but "theory" is much faster.
`u.old`	A matrix that contains initial left singular vectors as the columns of the matrix.
`v.old`	A matrix that contains initial right singular vectors as the columns of the matrix.
`gamma.u`	When the method="theory", gamma.u=sqrt(2) corresponds to the sqrt(2 log(p)), which is the largest magnitude of p iid standard normals. If gamma.u is manually set to be smaller or larger than sqrt2, the left singular vectors will be denser or sparser respectively.
`gamma.v`	When the method="theory", gamma.u=sqrt(2) corresponds to the sqrt(2 log(p)), which is the largest magnitude of p iid standard normals. If gamma.u is manually set to be smaller or larger than sqrt2, the right singular vectors will be denser or sparser respectively.
`dothres`	Dothres has two choices, either "hard" or "soft", which means hard-thresholding or soft-thresholding
`r`	A scaler, the number of components, i.e., the number of singular vectors to be computed.
`tol`	The tolerance level that determines when the algorithm stops.
`n.iter`	Maximum number of iterations allowed.
`n.boot`	Number of bootstrap to estimate the threshold level when method = "method"
`sigma`	Sigma is a scaler for the noise level. The user can set it to be NA, and the function will estimate it automatically.
`non.orth`	If non.orth=TRUE, then the last iteration of the algorithm will not involve orthoganolization, which should produce sparse solutions.

`u`	A matrix containing left singular vectors
`v`	A matrix containing right singular vectors
`d`	A vector containing singular values
`niter`	Number of iterations for the algorithm to converge
`sigma.hat`	An estimate of the noise level
`dist.u`	The distance between the left singular vectors of the last two iterations, can be used to see whether the algorithm indeed converges.
`dist.v`	The distance between the right singular vectors of the last two iterations, can be used to see whether the algorithm indeed converges.

Dan Yang

A Sparse SVD Method for High-dimensional Data

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ans.initial <- ssvd.initial(matrix(rnorm(2^15),2^7,2^8), method = "method")
ans.iter <- ssvd.iter.thresh(matrix(rnorm(2^15),2^7,2^8), 
u.old=ans.initial$u, v.old= ans.initial$v, method = "method")