Usage
ssvd(x, method = c("theory", "method"), alpha.method = 0.05, alpha.theory = 1.5,
huber.beta = 0.95, sigma = NA, r = 1, gamma.u = sqrt(2), gamma.v = sqrt(2),
dothres = "hard", tol = 1e-08, n.iter = 100, n.boot = 100, non.orth = FALSE)
Arguments
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.
alpha.method
Alpha.method is the level of the hypothesis test when one performs Holm multiple hypothesis testing, which is used to select the candidate rows and columns in the initialization step.
The value is usually set to be 0.05.
alpha.theory
Alpha.theory is a scaler that is used when normal assumption is true, method="theory", and a chisq tail bound is used to select the candidate rows and columns in the initialization step.
Most of the time, users should keep it as it is.
huber.beta
Huber.beta is a scaler which is the cut-off point in the Huber function. The huberization is utilized to achieve robustness when normal assumption is violated in the initialization step.
sigma
Sigma is a scaler for the noise level. The user can set it to be NA, and the function will estimate it automatically.
r
A scaler, the number of components, i.e., the number of singular vectors to be computed.
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.
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"
non.orth
If non.orth=TRUE, then the last iteration of the algorithm will not involve orthoganolization, which should produce sparse solutions.