pls: PCA and PLS

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

PCA and PLS

Description

Principal component (PCA) and partial least squares (PLS) analyses.

Function pca fits PCA models.

Functions pls fit PLS1 or PLS2 models.

Matrix X is centered before the analyses, but X is not column-wise scaled (there is no argument scale available). If a scaling is needed, the user has to scale X before using the functions.

Row observations can eventually be weighted with a priori weights (using argument weights).

Usage

pca(Xr, Xu = NULL, ncomp, algo = NULL, ...)

pls(Xr, Yr, Xu = NULL, ncomp, algo = NULL, ...)

Arguments

Xr	A n x p matrix or data frame of reference (= training) observations.
Yr	A n x q matrix or data frame, or a vector of length n, of reference (= training) responses.
Xu	A m x p matrix or data frame of new (= test) observations to be projected in the calculated reference score space (Xu is not used in the calculation of this score space). Default to NULL.
ncomp	The maximal number of PCA or PLS scores (= components = latent variables) to be calculated.
algo	For pca, a function (algorithm) implementing a PCA. Default to NULL: if n < p, pca_eigenk is used; in the other case, pca_eigen is used. For pls, a function implementing a PLS. Default to NULL (pls_kernel is used).
...	Optionnal arguments to pass in the function defined in algo.

Value

A list of outputs (see examples), such as:

Tr	The Xr-score matrix (n x ncomp).
Tu	The Xu-score matrix (m x ncomp).
P	The Xr-loadings matrix (p x ncomp).
explvar	Proportions of Xr-variance explained by the Xr-score space.

And other outputs: See the examples and function defined in algo.

Examples

n <- 10
p <- 6
set.seed(1)
X <- matrix(rnorm(n * p, mean = 10), ncol = p)
y1 <- 100 * rnorm(n)
y2 <- 100 * rnorm(n)
Y <- cbind(y1, y2)
set.seed(NULL)

Xr <- X[1:8, ] ; Yr <- Y[1:8, ] 
Xu <- X[9:10, ] ; Yu <- Y[9:10, ] 

##################### PCA

ncomp <- 3
fm <- pca(Xr, ncomp = ncomp)
names(fm)
fm$Tr   
fm$P

### Proportion of explained X-variance

z <- fm$explvar
z
barplot(100 * z$pvar, names.arg = paste("comp", z$ncomp), 
  ylab = "Pct. of variance explained")

### Scores

comp <- c(1, 2)
#comp <- c(2, 3)
plotxy(fm$Tr[, comp], zeroes = TRUE)

plotxy(fm$Tr[, comp], zeroes = TRUE, labels = TRUE)

### Contributions of the individuals (in proportions)

fm$contr.ind
colSums(fm$contr.ind)

### Loadings

plotxy(fm$P, zeroes = TRUE, label = TRUE)

### Coordonates of the variables

plotxy(fm$coord.var, zeroes = TRUE, label = TRUE)

### Contributions of the variables (in proportions)

fm$contr.var
colSums(fm$contr.var)

### Correlation circle

fm$cor.circle

plotxy(fm$cor.circle, zeroes = TRUE, labels = TRUE, circle = TRUE, ylim = c(-1, 1))

### Projection of Xu on the score space Tr ==> Scores Tu

fm <- pca(Xr, Xu, ncomp = ncomp)
Tr <- fm$Tr
Tu <- fm$Tu

T <- rbind(Tr, Tu)
row.names(T) <- 1:nrow(T)
group <- c(rep("Reference", nrow(Tr)), rep("Unknown", nrow(Tu)))
plotxy(T, group = group, pch = 16, zeroes = TRUE)
plotxy(T, group = group, labels = TRUE, zeroes = TRUE, alpha.f = 1)

##################### PLS

ncomp <- 3
fm <- pls(Xr, Yr, ncomp = ncomp)
names(fm)
fm$Tr
fm$P

### Proportion of explained X-variance

fm$explvarx

### Projection of Xu on the score space Tr ==> Scores Tu

fm <- pls(Xr, Yr, Xu, ncomp = ncomp)
fm$Tr
fm$Tu

mlesnoff/rnirs documentation built on April 24, 2023, 4:17 a.m.