| Type: | Package |
| Encoding: | UTF-8 |
| Title: | Canonical Correlation Analysis |
| Version: | 1.2.2 |
| Author: | Ignacio González, Sébastien Déjean |
| Maintainer: | Sébastien Déjean <sebastien.dejean@math.univ-toulouse.fr> |
| 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. |
| Depends: | R (≥ 2.10), fda, fields |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Repository: | CRAN |
| NeedsCompilation: | no |
| Packaged: | 2023-09-04 06:36:46 UTC; sdejean |
| Date/Publication: | 2023-09-05 08:10:13 UTC |
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 <sebastien.dejean@math.univ-toulouse.fr>
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 |
ycoef |
estimated coefficients for the 'Y' variables as returned by |
scores |
a list returned by the internal function |
Author(s)
Sébastien Déjean, Ignacio González
References
www.lsp.ups-tlse.fr/CCA
See Also
Examples
data(nutrimouse)
X=as.matrix(nutrimouse$gene[,1:10])
Y=as.matrix(nutrimouse$lipid)
res.cc=cc(X,Y)
plot(res.cc$cor,type="b")
plt.cc(res.cc)
Additional computations for CCA
Description
The comput() function can be viewed as an internal function. It is called by cc()
and rcc to perform additional computations. The user does not have to call it by himself.
Usage
comput(X, Y, res)
Arguments
X |
numeric matrix (n * p), containing the X coordinates. |
Y |
numeric matrix (n * q), containing the Y coordinates. |
res |
results provided by the |
Value
A list containing the following components:
xscores |
X canonical variates |
yscores |
Y canonical variates |
corr.X.xscores |
Correlation bewteen X and X canonical variates |
corr.Y.xscores |
Correlation bewteen Y and X canonical variates |
corr.X.yscores |
Correlation bewteen X and Y canonical variates |
corr.Y.yscores |
Correlation bewteen Y and Y canonical variates |
Author(s)
Sébastien Déjean, Ignacio González
See Also
Estimate the parameters of regularization
Description
Calulate the leave-one-out criterion on a 2D-grid to determine optimal values for the parameters of regularization.
Usage
estim.regul(X, Y, grid1 = NULL, grid2 = NULL, plt = TRUE)
Arguments
X |
numeric matrix (n * p), containing the X coordinates. |
Y |
numeric matrix (n * p), containing the X coordinates. |
grid1 |
vector defining the values of lambda1 to be tested. If
NULL, the vector is defined as |
grid2 |
vector defining the values of lambda2 to be tested. If
NULL, the vector is defined as |
plt |
logical argument indicating whether an image should be
plotted by calling the |
Value
A 3-vector containing the 2 values of the parameters of regularization on which the leave-one-out criterion reached its maximum; and the maximal value reached on the grid.
Author(s)
Sébastien Déjean, Ignacio González
See Also
Examples
#data(nutrimouse)
#X=as.matrix(nutrimouse$gene)
#Y=as.matrix(nutrimouse$lipid)
#res.regul = estim.regul(X,Y,c(0.01,0.5),c(0.1,0.2,0.3))
Plot the cross-validation criterion
Description
This function provide a visualization of the values of the
cross-validation criterion obtained on a grid defined in the function estim.regul().
Usage
img.estim.regul(estim)
Arguments
estim |
Object returned by |
Author(s)
Sébastien Déjean, Ignacio González
See Also
Image of correlation matrices
Description
Display images of the correlation matrices within and between two data matrices.
Usage
img.matcor(correl, type = 1)
Arguments
correl |
Correlation matrices as returned by the |
type |
character determining the kind of plots to be produced: either one ((p+q) * (p+q)) matrix or three matrices (p * p), (q * q) and (p * q) |
Details
Matrices are pre-processed before calling the image() function in order to
get, as in the numerical representation, the diagonal from upper-left corner to
bottom-right one.
Author(s)
Sébastien Déjean, Ignacio González
See Also
Examples
data(nutrimouse)
X=as.matrix(nutrimouse$gene)
Y=as.matrix(nutrimouse$lipid)
correl=matcor(X,Y)
img.matcor(correl)
img.matcor(correl,type=2)
Leave-one-out criterion
Description
The loo() function can be viewed as an internal
function. It is called by estim.regul() to obtain optimal values
for the two parameters of regularization.
Usage
loo(X, Y, lambda1, lambda2)
Arguments
X |
numeric matrix (n * p), containing the X coordinates. |
Y |
numeric matrix (n * q), containing the Y coordinates. |
lambda1 |
parameter of regularization for X variables |
lambda2 |
parameter of regularization for Y variables |
Author(s)
Sébastien Déjean, Ignacio González
See Also
Correlations matrices
Description
The function computes the correlation matrices within and between two datasets.
Usage
matcor(X, Y)
Arguments
X |
numeric matrix (n * p), containing the X coordinates. |
Y |
numeric matrix (n * q), containing the Y coordinates. |
Value
A list containing the following components:
Xcor |
Correlation matrix (p * p) for the X variables |
Ycor |
Correlation matrix (q * q) for the Y variables |
XYcor |
Correlation matrix ((p+q) * (p+q)) between X and Y variables |
Author(s)
Sébastien Déjean, Ignacio González
See Also
Examples
data(nutrimouse)
X=as.matrix(nutrimouse$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 |
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
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 |
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
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 |
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
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 |
ycoef |
estimated coefficients for the 'Y' variables as returned by |
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
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)