soplsrda: Block dimension reduction by SO-PLS-DA

Description

Function soplsrda implements dimension reductions of pre-selected blocks of variables (= set of columns) of a reference (= training) matrix, by sequential orthogonalization-PLS (said "SO-PLS") in a context of discrimination.

Function soplsrdacv perfoms repeteated cross-validation of an SO-PLS-RDA model in order to choose the optimal lv combination from the different blocks.

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 function allows giving a priori weights to the rows of the reference matrix in the calculations.

Insoplslda and soplsqda, probabilistic LDA and QDA are run over the PLS2 LVs, respectively.

Usage

soplsrda(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlv)
soplslda(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlv, 
prior = c("unif", "prop"))
soplsqda(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlv, 
prior = c("unif", "prop"))
soplsrdacv(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlvlist=list(), 
nbrep=30, cvmethod="kfolds", seed = 123, samplingk = NULL, nfolds = 7, 
optimisation = c("global","sequential")[1], 
criterion = c("err","rmse")[1], selection = c("localmin","globalmin","1std")[1])
soplsldacv(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlvlist=list(), 
prior = c("unif", "prop"), nbrep = 30, cvmethod = "kfolds", seed = 123, samplingk = NULL, 
nfolds = 7, optimisation = c("global","sequential")[1], 
criterion = c("err","rmse")[1], selection = c("localmin","globalmin","1std")[1])
soplsqdacv(Xlist, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL, nlvlist = list(), 
prior = c("unif", "prop"), nbrep = 30, cvmethod = "kfolds", seed = 123, samplingk = NULL, 
nfolds = 7, optimisation = c("global","sequential")[1], 
criterion = c("err","rmse")[1], selection = c("localmin","globalmin","1std")[1])
# S3 method for Soplsrda
transform(object, X, ...) 
# S3 method for Soplsprobda
transform(object, X, ...) 
# S3 method for Soplsrda
predict(object, X, ...) 
# S3 method for Soplsprobda
predict(object, X, ...)

Value

For soplsrda, soplslda, soplsqda:

fm: list with the PLS models: (T): X-scores matrix; (P): X-loading matrix;(R): The PLS projection matrix (p,nlv); (W): X-loading weights matrix ;(C): The Y-loading weights matrix; (TT): the X-score normalization factor; (xmeans): the centering vector of X (p,1); (ymeans): the centering vector of Y (q,1); (weights): vector of observation weights; (Xscales): X scaling values; (Yscales): Y scaling values; (U): intermediate output.
lev: classes
ni: number of observations in each class

For transform.Soplsrda, transform.Soplsprobda: the LVs Calculated for the new matrices list \(Xlist\) from the model.

For predict.Soplsrda, predict.Soplsprobda:

pred: predicted class for each observation
posterior: calculated probability of belonging to a class for each observation

For soplsrdacv, soplsldacv, soplsqdacv:

lvcombi: matrix or list of matrices, of tested component combinations.
optimCombiLine: number of the combination line corresponding to the optimal one. In the case of a sequential optimisation, it is the number of the combination line in the model with all the X-blocks.
optimcombi: the number of PLS components of each X-block allowing the optimisation of the mean rmseCV.
optimExplVarCV: cross-validated explained variance for the optimal soplsda model.
rmseCV: matrix or list of matrices of mean and sd of cross-validated rmse in the model for each combination and response variables.
ExplVarCV: matrix or list of matrices of mean and sd of cross-validated explained variances in the model for each combination and response variables.
errCV: matrix or list of matrices of mean and sd of cross-validated classification error rates in the model for each combination and response variables.

Arguments

Xlist: For the main functions: A list of matrices or data frames of reference (= training) observations.
X: For the auxiliary functions: list of new X-data, with the same variables than the training X-data.
y: Training class membership (\(n\)). Note: If y is a factor, it is replaced by a character vector.
Xscaling: vector (of length Xlist) of variable scaling for each datablock, among "none" (mean-centering only), "pareto" (mean-centering and pareto scaling), "sd" (mean-centering and unit variance scaling). If "pareto" or "sd", uncorrected standard deviation is used.
Yscaling: variable scaling for the Y-block, among "none" (mean-centering only), "pareto" (mean-centering and pareto scaling), "sd" (mean-centering and unit variance scaling). If "pareto" or "sd", uncorrected standard deviation is used.
weights: a priori weights to the rows of the reference matrix in the calculations.
nlv: 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.
nlvlist: A list of same length as the number of X-blocks. Each component of the list gives the number of PLS components of the corresponding X-block to test.
nbrep: An integer, setting the number of CV repetitions. Default value is 30.
cvmethod: "kfolds" for k-folds cross-validation, or "loo" for leave-one-out.
seed: a numeric. Seed used for the repeated resampling, and if cvmethod is "kfolds" and samplingk is not NULL.
samplingk: Optional. A vector of length n. The elements are the values of a qualitative variable used for stratified partition creation.
nfolds: An integer, setting the number of partitions to create. Default value is 7.
optimisation: "global" or "sequential" optimisation of the number of components. If "sequential", the optimal lv number is found for the first X-block, then for the 2nd one, etc...
criterion: optimisation criterion among "rmse" and "err" (for classification error rate)
selection: a character indicating the selection method to use to choose the optimal combination of components, among "localmin","globalmin","1std". If "localmin": the optimal combination corresponds to the first local minimum of the mean CV rmse or error rate. If "globalmin" : the optimal combination corresponds to the minimum mean CV rmse or error rate. If "1std" (one standard error rule) : it corresponds to the first combination after which the mean cross-validated rmse or error rate does not decrease significantly.
prior: The prior probabilities of the classes. Possible values are "unif" (default; probabilities are set equal for all the classes) or "prop" (probabilities are set equal to the observed proportions of the classes in y).
object: For the auxiliary functions: A fitted model, output of a call to the main functions.
...: For the auxiliary functions: Optional arguments. Not used.

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.

- Tenenhaus, M., 1998. La régression PLS: théorie et pratique. Editions Technip, Paris, France.

Examples

Run this code


N <- 10 ; p <- 12
set.seed(1)
X <- matrix(rnorm(N * p, mean = 10), ncol = p, byrow = TRUE)
y <- matrix(sample(c("1", "4", "10"), size = N, replace = TRUE), ncol=1)
colnames(X) <- paste("x", 1:ncol(X), sep = "")
set.seed(NULL)

n <- nrow(X)

X_list <- list(X[,1:4], X[,5:7], X[,9:ncol(X)])
X_list_2 <- list(X[1:2,1:4], X[1:2,5:7], X[1:2,9:ncol(X)])

# EXEMPLE WITH SO-PLS-RDA
soplsrdacv(X_list, y, Xscaling = c("none", "pareto", "sd")[1], 
Yscaling = c("none", "pareto", "sd")[1], weights = NULL,
nlvlist=list(0:1, 1:2, 0:1), nbrep=1, cvmethod="loo", seed = 123, 
samplingk = NULL, nfolds = 3, optimisation = "global", 
criterion = c("err","rmse")[1], selection = "localmin")

ncomp <- 2
fm <- soplsrda(X_list, y, nlv = ncomp)
predict(fm,X_list_2)
transform(fm,X_list_2)

ncomp <- c(2, 0, 3)
fm <- soplsrda(X_list, y, nlv = ncomp)
predict(fm,X_list_2)
transform(fm,X_list_2)

ncomp <- 0
fm <- soplsrda(X_list, y, nlv = ncomp)
predict(fm,X_list_2)
transform(fm,X_list_2)

# EXEMPLE WITH SO-PLS-LDA
ncomp <- 2
weights <- rep(1 / n, n)
#w <- 1:n
soplslda(X_list, y, Xscaling = "none", nlv = ncomp, weights = weights)
soplslda(X_list, y, Xscaling = "pareto", nlv = ncomp, weights = weights)
soplslda(X_list, y, Xscaling = "sd", nlv = ncomp, weights = weights)

fm <- soplslda(X_list, y, Xscaling = c("none","pareto","sd"), nlv = ncomp, weights = weights)
predict(fm,X_list_2)
transform(fm,X_list_2)