rchemo (version 0.1-3)

cglsr: CG Least Squares Models

Description

Conjugate gradient algorithm (CG) for the normal equations (CGLS algorithm 7.4.1, Bjorck 1996, p.289)

Usage

cglsr(X, y, nlv, reorth = TRUE, filt = FALSE)
# S3 method for Cglsr
coef(object, ..., nlv = NULL)  
# S3 method for Cglsr
predict(object, X, ..., nlv = NULL)

Value

For cglsr:

B

matrix with the model coefficients for the fix nlv.

gnew

squared norm of the s vector

xmeans

variable means for the training X-data

ymeans

variable means for the training Y-data

F

If filt = TRUE, the filter factors

For coef.Cglsr :

int

intercept value.

B

matrix with the model coefficients.

For predict.Cglsr :

pred

list of matrices, with the predicted values for each number nlv of CG iterations

Arguments

X

For the main function: Training X-data (\(n, p\)). --- For auxiliary functions: New X-data (\(m, p\)) to consider.

y

Univariate training Y-data (\(n, 1\)).

nlv

The number(s) of CG iterations.

reorth

Logical. If TRUE, a Gram-Schmidt reorthogonalization of the normal equation residual vectors is done.

filt

Logical. If TRUE, the filter factors are computed (output F).

object

For auxiliary functions: A fitted model, output of a call to the main functions.

...

For auxiliary functions: Optional arguments. Not used.

Details

The code for re-orthogonalization (Hansen 1998) and filter factors (Vogel 1987, Hansen 1998) computations is a transcription (with few adaptations) of the matlab function `cgls` (Saunders et al. https://web.stanford.edu/group/SOL/software/cgls/; Hansen 2008).

The filter factors can be used to compute the model complexity of CGLSR and PLSR models (see dfplsr_cg).

Data \(X\) and \(y\) are internally centered.

Missing values are not allowed.

References

Bjorck, A., 1996. Numerical Methods for Least Squares Problems, Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611971484

Hansen, P.C., 1998. Rank-Deficient and Discrete Ill-Posed Problems, Mathematical Modeling and Computation. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9780898719697

Hansen, P.C., 2008. Regularization Tools version 4.0 for Matlab 7.3. Numer Algor 46, 189-194. https://doi.org/10.1007/s11075-007-9136-9

Manne R. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics Intell. Lab. Syst. 1987; 2: 187-197.

Phatak A, De Hoog F. Exploiting the connection between PLS, Lanczos methods and conjugate gradients: alternative proofs of some properties of PLS. J. Chemometrics 2002; 16: 361-367.

Vogel, C. R., "Solving ill-conditioned linear systems using the conjugate gradient method", Report, Dept. of Mathematical Sciences, Montana State University, 1987.

Examples

z <- ozone$X
u <- which(!is.na(rowSums(z)))
X <- z[u, -4]
y <- z[u, 4]
dim(X)
headm(X)
Xtest <- X[1:2, ]
ytest <- y[1:2]

nlv <- 10
fm <- cglsr(X, y, nlv = nlv)

coef(fm)
coef(fm, nlv = 1)

predict(fm, Xtest)
predict(fm, Xtest, nlv = 1:3)

pred <- predict(fm, Xtest)$pred
msep(pred, ytest)

cglsr(X, y, nlv = 5, filt = TRUE)$F