gplssvd: Generalized partial least squares singular value...
In derekbeaton/GSVD: The generalized singular value decomposition

Description Usage Arguments Value Author(s) See Also Examples

gplssvd takes in left (XLW, YLW) and right (XRW, YRW) constraints (usually diagonal matrices, but any positive semi-definite matrix is fine) that are applied to each data matrix (X and Y), respectively. Right constraints for each data matrix are used for the orthogonality conditions.

1	gplssvd(X, Y, XLW, YLW, XRW, YRW, k = 0, tol = .Machine$double.eps)

`X`	a data matrix
`Y`	a data matrix
`XLW`	X's Left Weights – the constraints applied to the left side (rows) of the `X` matrix and thus left singular vectors.
`YLW`	Y's Left Weights – the constraints applied to the left side (rows) of the `Y` matrix and thus left singular vectors.
`XRW`	X's Right Weights – the constraints applied to the right side (columns) of the `X` matrix and thus right singular vectors.
`YRW`	Y's Right Weights – the constraints applied to the right side (columns) of the `Y` matrix and thus right singular vectors.
`k`	total number of components to return though the full variance will still be returned (see `d_full`). If 0, the full set of components are returned.
`tol`	default is .Machine$double.eps. A tolerance level for eliminating effectively zero (small variance), negative, imaginary eigen/singular value components.

A list with thirteen elements:

`d_full`	A vector containing the singular values of DAT above the tolerance threshold (based on eigenvalues).
`l_full`	A vector containing the eigen values of DAT above the tolerance threshold (`tol`).
`d`	A vector of length `min(length(d_full), k)` containing the retained singular values
`l`	A vector of length `min(length(l_full), k)` containing the retained eigen values
`u`	Left (rows) singular vectors. Dimensions are `nrow(DAT)` by k.
`p`	Left (rows) generalized singular vectors.
`fi`	Left (rows) component scores.
`lx`	Latent variable scores for rows of `X`
`v`	Right (columns) singular vectors.
`q`	Right (columns) generalized singular vectors.
`fj`	Right (columns) component scores.
`ly`	Latent variable scores for rows of `Y`

Derek Beaton

tolerance_svd, geigen and gsvd

 # Three "two-table" technique examples
 data(wine)
 X <- scale(wine$objective)
 Y <- scale(wine$subjective)

 ## Partial least squares (correlation)
 pls.res <- gplssvd(X, Y)


 ## Canonical correlation analysis (CCA)
 ### NOTE:
 #### This is not "traditional" CCA because of the generalized inverse.
 #### However the results are the same as standard CCA when data are not rank deficient.
 #### and this particular version uses tricks to minimize memory & computation
 cca.res <- gplssvd(
     X = MASS::ginv(t(X)),
     Y = MASS::ginv(t(Y)),
     XRW=crossprod(X),
     YRW=crossprod(Y)
 )


 ## Reduced rank regression (RRR) a.k.a. redundancy analysis (RDA)
 ### NOTE:
 #### This is not "traditional" RRR because of the generalized inverse.
 #### However the results are the same as standard RRR when data are not rank deficient.
 rrr.res <- gplssvd(
     X = MASS::ginv(t(X)),
     Y = Y,
     XRW=crossprod(X)
 )