Package 'CCA'

Title: Canonical Correlation Analysis
Description: Provides a set of functions that extend the 'cancor' function with new numerical and graphical outputs. It also include a regularized extension of the canonical correlation analysis to deal with datasets with more variables than observations.
Authors: Ignacio González, Sébastien Déjean
Maintainer: Sébastien Déjean <[email protected]>
License: GPL (>= 2)
Version: 1.2.2
Built: 2024-09-03 07:09:24 UTC
Source: CRAN

Help Index

Canonical correlation analysis

Description

The package provides a set of functions that extend the cancor() function with new numerical and graphical outputs. It includes a regularized extension of the canonical correlation analysis to deal with datasets with more variables than observations and enables to handle with missing values.

Author(s)

Ignacio Gonzalez, Sebastien Dejean Maintainer: Sebastien Dejean <[email protected]>

Canonical Correlation Analysis

Description

The function performs Canonical Correlation Analysis to highlight correlations between two data matrices. It complete the cancor() function with supplemental numerical and graphical outputs and can handle missing values.

Usage

cc(X, Y)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * q), containing the Y coordinates.

Details

The canonical correlation analysis seeks linear combinations of the 'X' variables which are the most correlated with linear combinations of the 'Y' variables.

Let PX and PY be the projector onto the respective column-space of X and Y. The eigenanalysis of PXPY provide the canonical correlations (square roots of the eigenvalues) and the coefficients of linear combinations that define the canonical variates (eigen vectors).

Value

A list containing the following components:

cor

canonical correlations
names

a list containing the names to be used for individuals and variables for graphical outputs
xcoef

estimated coefficients for the 'X' variables as returned by cancor()
ycoef

estimated coefficients for the 'Y' variables as returned by cancor()
scores

a list returned by the internal function comput() containing individuals and variables coordinates on the canonical variates basis.

Author(s)

Sébastien Déjean, Ignacio González

References

www.lsp.ups-tlse.fr/CCA

See Also

rcc, plt.cc

Examples

data(nutrimouse)
X=as.matrix(nutrimouse$gene[,1:10])
Y=as.matrix(nutrimouse$lipid)
res.cc=cc(X,Y)
plot(res.cc$cor,type="b")
plt.cc(res.cc)

Additional computations for CCA

Description

The comput() function can be viewed as an internal function. It is called by cc() and rcc to perform additional computations. The user does not have to call it by himself.

Usage

comput(X, Y, res)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * q), containing the Y coordinates.
res

results provided by the cc() and rcc() functions.

Value

A list containing the following components:

xscores

X canonical variates
yscores

Y canonical variates
corr.X.xscores

Correlation bewteen X and X canonical variates
corr.Y.xscores

Correlation bewteen Y and X canonical variates
corr.X.yscores

Correlation bewteen X and Y canonical variates
corr.Y.yscores

Correlation bewteen Y and Y canonical variates

Author(s)

Sébastien Déjean, Ignacio González

See Also

cc, rcc

Estimate the parameters of regularization

Description

Calulate the leave-one-out criterion on a 2D-grid to determine optimal values for the parameters of regularization.

Usage

estim.regul(X, Y, grid1 = NULL, grid2 = NULL, plt = TRUE)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * p), containing the X coordinates.
grid1

vector defining the values of lambda1 to be tested. If NULL, the vector is defined as seq(0.001, 1, length = 5)
grid2

vector defining the values of lambda2 to be tested. If NULL, the vector is defined as seq(0.001, 1, length = 5)
plt

logical argument indicating whether an image should be plotted by calling the img.estim.regul() function.

Value

A 3-vector containing the 2 values of the parameters of regularization on which the leave-one-out criterion reached its maximum; and the maximal value reached on the grid.

Author(s)

Sébastien Déjean, Ignacio González

See Also

loo

Examples

#data(nutrimouse)
#X=as.matrix(nutrimouse$gene)
#Y=as.matrix(nutrimouse$lipid)
#res.regul = estim.regul(X,Y,c(0.01,0.5),c(0.1,0.2,0.3))

Plot the cross-validation criterion

Description

This function provide a visualization of the values of the cross-validation criterion obtained on a grid defined in the function estim.regul().

Usage

img.estim.regul(estim)

Arguments

estim

Object returned by estim.regul().

Author(s)

Sébastien Déjean, Ignacio González

See Also

estim.regul

Image of correlation matrices

Description

Display images of the correlation matrices within and between two data matrices.

Usage

img.matcor(correl, type = 1)

Arguments

correl

Correlation matrices as returned by the matcor() function
type

character determining the kind of plots to be produced: either one ((p+q) * (p+q)) matrix or three matrices (p * p), (q * q) and (p * q)

Details

Matrices are pre-processed before calling the image() function in order to get, as in the numerical representation, the diagonal from upper-left corner to bottom-right one.

Author(s)

Sébastien Déjean, Ignacio González

See Also

matcor

Examples

data(nutrimouse)
X=as.matrix(nutrimouse$gene)
Y=as.matrix(nutrimouse$lipid)
correl=matcor(X,Y)
img.matcor(correl)
img.matcor(correl,type=2)

Leave-one-out criterion

Description

The loo() function can be viewed as an internal function. It is called by estim.regul() to obtain optimal values for the two parameters of regularization.

Usage

loo(X, Y, lambda1, lambda2)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * q), containing the Y coordinates.
lambda1

parameter of regularization for X variables
lambda2

parameter of regularization for Y variables

Author(s)

Sébastien Déjean, Ignacio González

See Also

estim.regul

Correlations matrices

Description

The function computes the correlation matrices within and between two datasets.

Usage

matcor(X, Y)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * q), containing the Y coordinates.

Value

A list containing the following components:

Xcor

Correlation matrix (p * p) for the X variables
Ycor

Correlation matrix (q * q) for the Y variables
XYcor

Correlation matrix ((p+q) * (p+q)) between X and Y variables

Author(s)

Sébastien Déjean, Ignacio González

See Also

img.matcor

Examples

data(nutrimouse)
X=as.matrix(nutrimouse$gene)
Y=as.matrix(nutrimouse$lipid)
correl=matcor(X,Y)
img.matcor(correl)
img.matcor(correl,type=2)

Nutrimouse dataset

Description

The nutrimouse dataset comes from a nutrition study in the mouse. It was provided by Pascal Martin from the Toxicology and Pharmacology Laboratory (French National Institute for Agronomic Research).

Usage

data(nutrimouse)

Format

A list containing the following components:

  • gene: data frame (40 * 120) with numerical variables

  • lipid: data frame (40 * 21) with numerical variables

  • diet: factor vector (40)

  • genotype: factor vector (40)

Details

Two sets of variables were measured on 40 mice:

  • expressions of 120 genes potentially involved in nutritional problems.

  • concentrations of 21 hepatic fatty acids.

    The 40 mice were distributed in a 2-factors experimental design (4 replicates):

  • Genotype (2-levels factor): wild-type and PPARalpha -/-

  • Diet (5-levels factor): Oils used for experimental diets preparation were corn and colza oils (50/50) for a reference diet (REF), hydrogenated coconut oil for a saturated fatty acid diet (COC), sunflower oil for an Omega6 fatty acid-rich diet (SUN), linseed oil for an Omega3-rich diet (LIN) and corn/colza/enriched fish oils for the FISH diet (43/43/14).

Source

P. Martin, H. Guillou, F. Lasserre, S. Déjean, A. Lan, J-M. Pascussi, M. San Cristobal, P. Legrand, P. Besse, T. Pineau - Novel aspects of PPARalpha-mediated regulation of lipid and xenobiotic metabolism revealed through a nutrigenomic study. Hepatology, in press, 2007.

References

www.inra.fr/internet/Centres/toulouse/pharmacologie/pharmaco-moleculaire/acceuil.html

Examples

data(nutrimouse)
boxplot(nutrimouse$lipid)

Graphical outputs for canonical correlation analysis

Description

This function calls either plt.var() or plt.indiv() or both functions to provide individual and/or variable representation on the canonical variates.

Usage

plt.cc(res, d1 = 1, d2 = 2, int = 0.5, type = "b", ind.names = NULL,
var.label = FALSE, Xnames = NULL, Ynames = NULL)

Arguments

res

Object returned by cc() or rcc()
d1

The dimension that will be represented on the horizontal axis
d2

The dimension that will be represented on the vertical axis
int

The radius of the inner circle
type

Character "v" (variables), "i" (individuals) or "b" (both) to specifying the plot to be done.
ind.names

vector containing the names of the individuals
var.label

logical indicating whether label should be plotted on the variables representation
Xnames

vector giving the names of X variables
Ynames

vector giving the names of Y variables

Author(s)

Sébastien Déjean, Ignacio González

References

www.lsp.ups-tlse.fr/Biopuces/CCA

See Also

plt.indiv, plt.var

Examples

data(nutrimouse)
X=as.matrix(nutrimouse$gene[,1:10])
Y=as.matrix(nutrimouse$lipid)
res.cc=cc(X,Y)
plt.cc(res.cc)
plt.cc(res.cc,d1=1,d2=3,type="v",var.label=TRUE)

Individuals representation for CCA

Description

This function provides individuals representation on the canonical variates.

Usage

plt.indiv(res, d1, d2, ind.names = NULL)

Arguments

res

Object returned by cc() or rcc()
d1

The dimension that will be represented on the horizontal axis
d2

The dimension that will be represented on the vertical axis
ind.names

vector containing the names of the individuals

Author(s)

Sébastien Déjean, Ignacio González

References

www.lsp.ups-tlse.fr/Biopuces/CCA

See Also

plt.var, plt.cc

Variables representation for CCA

Description

This function provides variables representation on the canonical variates.

Usage

plt.var(res, d1, d2, int = 0.5, var.label = FALSE, Xnames = NULL, Ynames = NULL)

Arguments

res

Object returned by cc or rcc
d1

The dimension that will be represented on the horizontal axis
d2

The dimension that will be represented on the vertical axis
int

The radius of the inner circle
var.label

logical indicating whether label should be plotted on the variables representation
Xnames

vector giving the names of X variables
Ynames

vector giving the names of Y variables

Author(s)

Sébastien Déjean, Ignacio González

References

www.lsp.ups-tlse.fr/Biopuces/CCA

See Also

plt.indiv, plt.cc

Regularized Canonical Correlation Analysis

Description

The function performs the Regularized extension of the Canonical Correlation Analysis to seek correlations between two data matrices when the number of columns (variables) exceeds the number of rows (observations)

Usage

rcc(X, Y, lambda1, lambda2)

Arguments

X

numeric matrix (n * p), containing the X coordinates.
Y

numeric matrix (n * q), containing the Y coordinates.
lambda1

Regularization parameter for X
lambda2

Regularization parameter for Y

Details

When the number of columns is greater than the number of rows, the matrice X'X (and/or Y'Y) may be ill-conditioned. The regularization allows the inversion by adding a term on the diagonal.

Value

A list containing the following components:

corr

canonical correlations
names

a list containing the names to be used for individuals and variables for graphical outputs
xcoef

estimated coefficients for the 'X' variables as returned by cancor()
ycoef

estimated coefficients for the 'Y' variables as returned by cancor()
scores

a list returned by the internal function comput() containing individuals and variables coordinates on the canonical variates basis.

Author(s)

Sébastien Déjean, Ignacio González

References

Leurgans, Moyeed and Silverman, (1993). Canonical correlation analysis when the data are curves. J. Roy. Statist. Soc. Ser. B. 55, 725-740.

Vinod (1976). Canonical ridge and econometrics of joint production. J. Econometr. 6, 129-137.

See Also

cc, estim.regul, plt.cc

Examples

data(nutrimouse)
X=as.matrix(nutrimouse$gene)
Y=as.matrix(nutrimouse$lipid)
res.cc=rcc(X,Y,0.1,0.2)
plt.cc(res.cc)