wsvd: Weighted Singular Value Decomposition
In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description Usage Arguments Value References Examples

The singular value decomposition of a matrix X solves the equation X = UDV', where U is the matrix of left singular vectors, D is a diagonal matrix of singular values (δ), and V is a matrix of right singular vectors.

Note that U is equivalent to the eigenvectors of the matrix XX' and V is equivalent to the eigenvectors of the matrix X'X. This implementation of singular value decomposition has three main features:

The decomposition of X is sped up by first computing the SVD of either XX' (p>n) or X'X (p<n), rather than that of X. For the case of p>n, this is XX' = U D^2 U', and for the case of p<n, this is X'X = V D^2 V'. This respectively gives the left or right singular vectors. For p>n, the right singular vectors are then obtained via V = X'UD^-1, and for p<n the left singular vectors are obtained via U = X'VD^-1. The reason this approach improves speed of calculation for large data sets is that the SVD is only performed on a matrix with min(n,p) by min(n,p) dimensions, which can be substantially faster than performing SVD on a data set n by p dimensions.
The observations going into the SVD are allowed to be weighted. Currently weights on the variables are not implemented. The weighted left singular vectors are defined as Ω = W^-0.5U. The resulting singular values Δ are then the singular values of the weighted data matrix Φ, where Φ = Ω Δ V'.
Only the singular values and singular vectors corresponding to δ > tol, where tol is a tolerance for small values. Values less than or equal to tol are considered to be zero.

1	wsvd(x, weights = NULL, method = c("dc", "std"), tol = 1e-04)

`x`	a matrix
`weights`	row weights. defaults to equal weights and returns the typical SVD.
`method`	whether the divide and conquer ("dc") or standard ("std") algorithm should be used for the SVD.
`tol`	tolerance for small singular values. values <= tol are considered zero and truncated.