blocksopls: Block dimension reduction by SO-PCA or SO-PLS

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

Block dimension reduction by SO-PCA or SO-PLS

Description

Functions blocksopca and blocksopls implement dimension reductions of pre-selected blocks of variables (= set of columns) of a reference (= training) matrix and eventually a new (= test) matrix, by sequential orthogonalization with PCA or PLS (so-called "SO-PCA" and "SO-PLS"), respectively.

SO-PLS is described for instance in Menichelli et al. 2014, Biancolillo et al. 2015 and Biancolillo 2016. SO-PCA uses the same approach but replacing PLS by PCA. In this last case, response variables Y are not required. The block reduction consists in calculating latent variables (= scores) for each block, each block being sequentially orthogonalized to the information computed from the previous blocks.

The scores calculated for the different blocks of the reference matrix are concatenated into a new output matrix. The same is done for the eventual test matrix.

The functions allow giving a priori weights to the rows of the reference matrix in the calculations (add argument weights within the optional arguments "...").

Usage

blocksopca(Xr, Xu = NULL, ncomp, blocks, colblocks = NULL, ...)

blocksopls(Xr, Yr, Xu = NULL, ncomp, blocks, colblocks = 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, which receives the same block-scaling as Xr (Xu is not used in the calculation of the block score spaces). Default to NULL.
ncomp	A vector of same length as the number of blocks defining the number of scores to calculate for each block, or a single number. In this last case, the same number of scores is used for all the blocks. If some Components of ncomp are equal to 0, the corresponding blocks are not considered.
blocks	A list of same length as the number of blocks. Each component of the list gives the column numbers in Xr defining the given block. The same blocks are used for Xu. Argument blocks can be replaced by argument colblocks.
colblocks	Alternative to argument blocks. A numeric vector of length p giving the index of the block for each of the columns of Xr (the same vector is used for Xu). Default to NULL (argument blocks is used).
...	Other arguments to pass in functions pca or pls.

Value

Tr	A matrix with the scores calculated from Xr and concatenated by block.
Tu	A matrix with the scores calculated from Xu and then concatenated by block. NULL if Xu = NULL.
blocks	A list of column numbers defining the blocks in the output matrices Tr and Tu (= lsit of the block indexes for the scores).
Fitr and Fitu	For SO-PLS. Y-response predictions for the reference and new observations.

References

- Biancolillo et al. , 2015. Combining SO-PLS and linear discriminant analysis for multi-block classification. Chemometrics and Intelligent Laboratory Systems, 141, 58-67.

- Biancolillo, A. 2016. Method development in the area of multi-block analysis focused on food analysis. PhD. University of copenhagen.

- Menichelli et al., 2014. SO-PLS as an exploratory tool for path modelling. Food Quality and Preference, 36, 122-134.

Examples

N <- 10 ; p <- 12
set.seed(1)
X <- matrix(rnorm(N * p, mean = 10), ncol = p, byrow = TRUE)
Y <- matrix(rnorm(N * 2, mean = 10), ncol = 2, byrow = TRUE)
colnames(X) <- paste("x", 1:ncol(X), sep = "")
colnames(Y) <- paste("y", 1:ncol(Y), sep = "")
set.seed(NULL)
X
Y

Xr <- X[1:8, ]
Yr <- Y[1:8, ]

Xu <- X[9:10, ]
Yu <- Y[9:10, ]

n <- nrow(Xr)
m <- nrow(Xu)

blocks <- list(1:4, 5:7, 9:ncol(X))
blocks

ncomp <- 2
blocksopls(Xr, Yr, Xu, blocks, ncomp = ncomp)

ncomp <- c(2, 0, 3)
blocksopls(Xr, Yr, Xu, blocks, ncomp = ncomp)
u <- which(ncomp > 0)
blocksopls(Xr, Yr, Xu, ncomp = ncomp[u], blocks = blocks[u])

ncomp <- 0
blocksopls(Xr, Yr, Xu, blocks, ncomp = ncomp)

######################### Syntax with weights

ncomp <- 2
w <- rep(1 / n, n)
#w <- 1:n
blocksopls(Xr, Yr, Xu, blocks, ncomp = ncomp, weights = w)

#########################  Syntax for a SO-PLSR

data(datcass)

Xr <- datcass$Xr
yr <- datcass$yr

Xu <- datcass$Xu
yu <- datcass$yu

######## With a LMR on the SO-PLS scores
######## This is the usual SO-PLSR

blocks <- list(1:500, 501:1050)
ncomp <- c(10, 5)
zfm <- blocksopls(Xr, yr, Xu, blocks, ncomp = ncomp)
names(zfm)

fm <- lmr(zfm$Tr, yr, zfm$Tu, yu)
headm(fm$fit)
mse(fm)
plot(fm$fit$y1, fm$y$y1)
abline(0, 1)

## Note: Above, if needed, the LMR predictions fm$fit 
## are already available in zfm$Fitu

head(cbind(fm$fit, zfm$Fitu))

######## With a PLSR on the SO-PLS scores

ncomp <- c(10, 5)
zfm <- blocksopls(Xr, yr, Xu, blocks, ncomp = ncomp)

fm <- plsr(zfm$Tr, yr, zfm$Tu, yu, ncomp = ncol(zfm$Tr))
headm(fm$fit)

z <- mse(fm, ~ ncomp)
plotmse(z)
z[z$msep == min(z$msep), ]

zncomp <- z$ncomp[z$msep == min(z$msep)][1]
y <- fm$y
fit <- fm$fit
plot(fit$y1[fit$ncomp == zncomp], y$y1[y$ncomp == zncomp])
abline(0, 1)

#########################  Syntax for a SO-PLSDA

data(datforages)

Xr <- datforages$Xr
yr <- datforages$yr

Xu <- datforages$Xu
yu <- datforages$yu

table(yr)
table(yu)

blocks <- list(1:350, 351:700)
ncomp <- 10
zfm <- blocksopls(Xr, dummy(yr), Xu, blocks, ncomp = ncomp)

######## With a probalistic DA on the SO-PLS scores
## (Any other DA, PLS-DA, etc. could be implemneted insteas)

fm <- daprob(zfm$Tr, yr, zfm$Tu, yu)
headm(fm$fit)
err(fm)

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