dual.spls (version 0.1.4)

d.spls.calval: Splits data into calibration and validation sets using the splitting method CalValXy that takes into account X and y

Description

The function d.spls.calval divides the data X into a calibration and a validation. It uses a variation on the Kennard and Stone strategy CalValXy by dividing observations into groups (see details for more explanations).

Usage

d.spls.calval(X,pcal=NULL,Datatype=NULL,y=NULL,ncells=10,Listecal=NULL,
center=TRUE,method="euclidean",pc=0.9)

Value

A list of the following attributes

indcal

a numeric vector giving the row indices of the input data selected for calibration.

indval

a numeric vector giving the row indices of the remaining observations.

Arguments

X

a numeric matrix of predictors values.

pcal

a positive integer between 0 and 100. pcal is the percentage of calibration samples to be selected. Default value is NULL, meaning as long as Listecal is specified, pcal is not necessary.

Datatype

A vector of index specifying each observation belonging to which group index. Default value is NULL, meaning the function will use the internal function type to compute the vector for ncells. If NULL, parameter y should be specified. (see details for more explanation)

y

a numeric vector of responses. Default value is NULL, meaning as long as Datatype is specified, y is not necessary.

ncells

a positive integer. ncells is the number of groups dividing the observations. If Datatype is not specified, the function divides the observations into ncells groups. Default value is 10.

Listecal

a numeric vector specifying how many observations from each group should be selected as calibration. Default value is NULL, meaning the function will consider a percentage of pcal from each group to be in the calibration set. If NULL, parameter pcal should be specified.

center

logical value indicating wether the matrix X should be centered. Default set to TRUE.

method

the method and norm used for the distance computation. It is by default equal to "euclidean" which means original X is used with euclidean norm. "svd-euclidean" means euclidean distance is used after a SVD transformation with pc components. "pca-euclidean" means euclidean distance on PCA scores with pc components. For

pc

a positive real value indicating the number of component to consider when applying the SVD transformation or the PCA. If pc \(< 1\), the number of components kept corresponds to the number of components explaining at least (pc \(< 1\)) percent of the total variance.

Author

Louna Alsouki François Wahl

Details

The algorithm allows to select samples using the classical Kennard and Stone on each group of observations one by one. It starts by selecting the point that is the furthest away from the centroid. This point is assigned as the calibration set and is removed from the list of candidates. Then, it identifies to which group belongs this first observation and considers the group \(g\) that comes after. It computes the distance \(\delta_{P_{i,g}}\) between the remaining points \(P_{i,g}\) belonging to the group the group \(g\) and the calibration point assigned. The point with the largest \(\delta_{P_{i,g}}\) is selected and removed from the set then the procedure moves on to the group that comes after.

When there is more than one calibration sample, the procedure computes the distance between each \(P_{i,g}\) from the concerned group and each \(P_{i,cal}\) from the calibration set. The minimal distance for each \(P_{i,g}\) is noted \(distmin(P_{i,g})\). The selected final candidate verifies the following equation: $$P_{selected}=\{ P_{i,g} | max(distmin(P_{i,g}))\} $$

Once each of the vector Listecal elements are null; the procedure is done.

The algorithm for only one group corresponds to the classical Kennard and Stone algorithm.

If Datatype is not specified, the function devides the observations into ncells groups. First, the observations are sorted according to the values of \(y\). Second, the observations is divided into equal ncells according to the cumulative empirical probabilities. Finally, each observation with a value of \(y\) belonging to a sub interval is assigned the number of the corresponding cell.

References

Kennard, Ronald W, and Larry A Stone. 1969. “Computer Aided Design of Experiments.” Technometrics 11 (1): 137–48.

See Also

d.spls.split,d.spls.type,d.spls.listecal

Examples

### load dual.spls library
library(dual.spls)
### parameters
n <- 100
p <- 50
nondes <- 20
sigmaondes <- 0.5
data=d.spls.simulate(n=n,p=p,nondes=nondes,sigmaondes=sigmaondes)

X <- data$X
y <- data$y

###calibration parameters for split1
pcal <- 70
ncells <- 3

split1 <- d.spls.calval(X=X,pcal=pcal,y=y,ncells=ncells)

###plotting split1
plot(X[split1$indcal,1],X[split1$indcal,2],xlab="Variable 1",
ylab="Variable 2",pch=19,col="red",main="Calibration and validation split1")
points(X[split1$indval,1],X[split1$indval,2],pch=19,col="green")
legend("topright", legend = c("Calibration points", "Validation points"),
cex = 0.8, col = c("red","green"), pch = c(19,19))

###calibration parameters for split2
ncells <- 3
dimtype=floor(n/3)
# type of observations
Datatype <- c(rep(1,dimtype),rep(2,dimtype),rep(3,(n-dimtype*2)))
# how many observations of each type are to be selected in the calibration set
L1=floor(0.7*length(which(Datatype==1)))
L2=floor(0.8*length(which(Datatype==2)))
L3=floor(0.6*length(which(Datatype==3)))
Listecal <- c(L1,L2,L3)

split2 <- d.spls.calval(X=X,y=y,Datatype=Datatype,Listecal=Listecal)

###plotting split2
plot(X[split2$indcal,1],X[split2$indcal,2],xlab="Variable 1",
ylab="Variable 2",pch=19,col="red",main="Calibration and validation split2")
points(X[split2$indval,1],X[split2$indval,2],pch=19,col="green")
legend("topright", legend = c("Calibration points", "Validation points"),
cex = 0.8, col = c("red","green"), pch = c(19,19))