cglsr: CG Least Squares Models

In mlesnoff/rchemo: Dimension reduction, Regression and Discrimination for Chemometrics

CG Least Squares Models

Description

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

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.

Usage

cglsr(X, y, nlv, reorth = TRUE, filt = FALSE)

## S3 method for class 'Cglsr'
coef(object, ..., nlv = NULL)  

## S3 method for class 'Cglsr'
predict(object, X, ..., nlv = NULL)  

Arguments

X	For 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	A fitted model, output of a call to the main functions.
...	Optional arguments. Not used.

Value

See the examples.

References

Björck, 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)))    ## Removing rows with NAs
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

## Comparison with PLSR algorithms

nlv <- 12
fm1 <- plskern(X, y, nlv = nlv)
fm2 <- plsnipals(X, y, nlv = nlv)
cbind(coef(fm1)$B, coef(fm2)$B,
      cglsr(X, y, nlv = nlv, reorth = TRUE)$B[, nlv],
      cglsr(X, y, nlv = nlv, reorth = FALSE)$B[, nlv])

mlesnoff/rchemo documentation built on April 15, 2023, 1:25 p.m.