rgcca  R Documentation 
RGCCA is a general statistical framework for multiblock data analysis. The rgcca() function implements this framework and is the main entry point of the package.
rgcca(
blocks,
connection = NULL,
tau = 1,
ncomp = 1,
scheme = "factorial",
scale = TRUE,
init = "svd",
bias = TRUE,
tol = 1e08,
verbose = FALSE,
scale_block = "inertia",
method = "rgcca",
sparsity = 1,
response = NULL,
superblock = FALSE,
NA_method = "na.ignore",
quiet = TRUE,
n_iter_max = 1000,
comp_orth = TRUE,
A = NULL,
C = NULL
)
blocks 
A list that contains the 
connection 
A ( 
tau 
Either a numerical value, a numeric vector of size
If tau is a numerical value, tau is identical across all constraints applied to all block weight vectors. If tau is a vector, tau[j] is used for the constraints applied to
all the block weight vectors associated to block If tau is a matrix, tau[k, j] is associated with the constraints
applied to the kth block weight vector corresponding to block
If tau = "optimal" the regularization parameters are estimated for each block and each dimension using the Schafer and Strimmer (2005) analytical formula. The tau parameters can also be estimated using rgcca_permutation or rgcca_cv. 
ncomp 
A numerical value or a vector of length 
scheme 
A string or a function specifying the scheme function applied to covariance maximization among "horst" (the identity function), "factorial" (the square function  default value), "centroid" (the absolute value function). The scheme function can be any continuously differentiable convex function and it is possible to design explicitly the scheme function (e.g. function(x) x^4) as argument of the function. See (Tenenhaus et al, 2017) for details. 
scale 
A logical value indicating if variables are standardized. 
init 
A string giving the type of initialization to use in the RGCCA algorithm. It could be either by Singular Value Decompostion ("svd") or by random initialization ("random") (default: "svd"). 
bias 
A logical value for biased ( 
tol 
The stopping value for the convergence of the algorithm (default: tol = 1e08). 
verbose 
A logical value indicating if the progress of the algorithm is reported while computing. 
scale_block 
A logical value or a string indicating if each block is scaled. If TRUE or "inertia", each block is divided by the sum of eigenvalues of its empirical covariance matrix. If "lambda1", each block is divided by the square root of the highest eigenvalue of its empirical covariance matrix. If standardization is applied (scale = TRUE), the block scaling applies on the standardized blocks. 
method 
A string specifying which multiblock component method to consider. Possible values are found using available_methods. 
sparsity 
Either a numerical value, a numeric vector of
size If sparsity is a numerical value, then sparsity is identical across all constraints applied to all block weight vectors. If sparsity is a vector, sparsity[j] is identical across the constraints
applied to the block weight vectors associated to block
If sparsity is a matrix, sparsity[k, j] is associated with the constraints
applied to the kth block weight vector corresponding to block
The sparsity parameter can be estimated by using rgcca_permutation or rgcca_cv. 
response 
A numerical value giving the position of the response block. When the response argument is filled, the supervised mode is automatically activated. 
superblock 
A logical value indicating if the superblock option is used. 
NA_method 
A string indicating the method used for handling missing values ("na.ignore", "na.omit"). (default: "na.ignore").

quiet 
A logical value indicating if some diagnostic messages are reported. 
n_iter_max 
Integer giving the algorithm's maximum number of iterations. 
comp_orth 
A logical value indicating if the deflation should lead to orthogonal block components or orthogonal block weight vectors. 
A 
Deprecated argument, please use blocks instead. 
C 
Deprecated argument, please use connection instead. 
Given J
data matrices
\mathbf X_1, \mathbf X_2, \dots, \mathbf X_J
that represent J
sets of variables
observed on the same set of n
individuals. These matrices
\mathbf X_1, \mathbf X_2, \dots, \mathbf X_J
,
called blocks must have the same number of rows, but may (and usually will)
have different numbers of columns.
RGCCA aims to study the relationships between these J
blocks.
It constitutes a general framework for many multiblock component methods
(see Tenenhaus and Tenenhaus, 2011 ; Tenenhaus et al. 2017). It combines the
power of multiblock data analysis methods (maximization of well identified
criteria) and the flexibility of PLS path modeling (the researcher decides
which blocks are connected and which are not). Hence, the use of RGCCA
requires the construction (user specified) of a design matrix
\mathbf C
that
characterizes the connections between blocks. Elements of the (symmetric)
design matrix \mathbf C = (c_{jk})
are positive (and usually equal to 1 if blocks j
and k
are connected, and 0 otherwise).
The rgcca() function implements
a monotone global convergent algorithm: the bounded criteria to be
maximized increases at each step of the iterative procedure and hits, at
convergence, a stationary point of the RGCCA optimization problem.
Moreover,
when the tau argument is used, depending on the dimensionality of each block
\mathbf X_j, j = 1, \ldots, J
,
the primal algorithm (when n \geq p_j
) or the dual algorithm
(when n < p_j
) is used (see Tenenhaus et al. 2015).
When sparsity is specified SGCCA, extends RGCCA to address the issue of variable selection (Tenenhaus et al, 2014). Specifically, RGCCA is combined with an L1penalty that gives rise to Sparse GCCA (SGCCA). The SGCCA algorithm is very similar to the RGCCA algorithm and keeps the same convergence properties (i.e. the bounded criteria to be maximized increases at each step of the iterative procedure and hits at convergence a stationary point).
At last, a deflation strategy can be used to compute several block components (specified by ncomp) per block. Within each block, components or weight vectors are guaranteed to be orthogonal. It should be noted that the numbers of components per block can differ from one block to another.
The rgcca() function handle missing values (punctual or blockwise missing structure) using the algorithm described in (Tenenhaus et al, 2005).
Guidelines describing how to use RGCCA in practice are provided in (Garali et al., 2018).
A fitted rgcca object.
Y 
A list of 
a 
A list of 
astar 
A list of 
crit 
A list of vector of length max(ncomp). Each vector of the list is related to one specific deflation stage and reports the values of the criterion for this stage across iterations. 
primal_dual 
A vector of length J. Element 
AVE 
A list of numerical values giving the indicators of model quality based on the Average Variance Explained (AVE): AVE(for each block), AVE(outer model), AVE(inner model). 
optimal 
A logical value indicating if the Schaffer and Strimmer formula was applied for estimating the optimal tau parameters. 
opt 
A list containing some options of the fitted RGCCA object. 
call 
Call of the function. 
blocks 
A list that contains the 
Garali I, Adanyeguh IM, Ichou F, Perlbarg V, Seyer A, Colsch B, Moszer I, Guillemot V, Durr A, Mochel F, Tenenhaus A. (2018) A strategy for multimodal data integration: application to biomarkers identification in spinocerebellar ataxia. Briefings in Bioinformatics. 19(6):13561369.
Tenenhaus M., Tenenhaus A. and Groenen P. J. (2017). Regularized generalized canonical correlation analysis: a framework for sequential multiblock component methods. Psychometrika, 82(3), 737777.
Tenenhaus A., Philippe C. and Frouin, V. (2015). Kernel generalized canonical correlation analysis. Computational Statistics and Data Analysis, 90, 114131.
Tenenhaus A., Philippe C., Guillemot V., Le Cao K. A., Grill J. and Frouin, V. (2014), Variable selection for generalized canonical correlation analysis, Biostatistics, 15(3), pp. 569583.
Tenenhaus A. and Tenenhaus M., (2011). Regularized Generalized Canonical Correlation Analysis, Psychometrika, 76(2), pp 257284.
Tenenhaus, M., Vinzi, V. E., Chatelin, Y. M., & Lauro, C. (2005). PLS path modeling. Computational statistics & data analysis, 48(1), 159205.
Schafer J. and Strimmer K. (2005). A shrinkage approach to largescale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology 4:32.
Arnaud Gloaguen, Vincent Guillemot, Arthur Tenenhaus. An efficient algorithm to satisfy l1 and l2 constraints. 49emes Journees de Statistique, May 2017, Avignon, France. (hal01630744)
plot.rgcca
, summary.rgcca
,
rgcca_cv
,
rgcca_permutation
rgcca_predict
####################
# Example 1: RGCCA #
####################
# Create the dataset
data(Russett)
blocks < list(
agriculture = Russett[, seq(3)],
industry = Russett[, 4:5],
politic = Russett[, 6:11]
)
politic < as.factor(apply(Russett[, 9:11], 1, which.max))
# RGCCA with default values : Blocks are fully connected, factorial scheme
# tau = 1 for all blocks, one component per block.
fit_rgcca < rgcca(blocks = blocks)
print(fit_rgcca)
plot(fit_rgcca, type = "weight", block = 1:3)
plot(fit_rgcca,
type = "sample", block = 1:2,
comp = rep(1, 2), resp = politic
)
############################################
# Example 2: RGCCA and multiple components #
############################################
# By default rgcca() returns orthogonal block components.
fit_rgcca < rgcca(blocks,
method = "rgcca",
connection = 1  diag(3),
superblock = FALSE,
tau = rep(1, 3),
ncomp = c(2, 2, 2),
scheme = "factorial",
comp_orth = TRUE,
verbose = TRUE
)
print(fit_rgcca)
plot(fit_rgcca,
type = "sample", block = 1,
comp = 1:2, resp = politic
)
plot(fit_rgcca, type = "weight",
block = 1:3, display_order = FALSE)
##############################
# Example 3: MCOA with RGCCA #
##############################
fit_rgcca < rgcca(blocks, method = "mcoa", ncomp = 2)
print(fit_rgcca)
# biplot representation
plot(fit_rgcca, type = "biplot", block = 4, resp = politic)
## Not run:
####################################
# Example 4: RGCCA and permutation #
####################################
# Tune the model to find the best set of tau parameters.
# By default, blocks are fully connected.
set.seed(27) #favorite number
perm_out < rgcca_permutation(blocks,
n_cores = 1,
par_type = "tau",
n_perms = 50
)
print(perm_out)
plot(perm_out)
# all the parameters were imported from a fitted permutation object
fit_rgcca < rgcca(perm_out)
print(fit_rgcca)
#######################################
# Example 5: RGCCA and dual algorithm #
#######################################
# Download the dataset's package at http://biodev.cea.fr/sgcca/ and install
# it from the package archive file.
# You can do it with the following R commands:
if (!("gliomaData" %in% rownames(installed.packages()))) {
destfile < tempfile()
download.file(
"http://biodev.cea.fr/sgcca/gliomaData_0.4.tar.gz", destfile
)
install.packages(destfile, repos = NULL, type = "source")
}
data("ge_cgh_locIGR", package = "gliomaData")
blocks < ge_cgh_locIGR$multiblocks
Loc < factor(ge_cgh_locIGR$y)
levels(Loc) < colnames(ge_cgh_locIGR$multiblocks$y)
blocks[[3]] < Loc
sapply(blocks, NCOL)
# rgcca algorithm using the dual formulation for X1 and X2
# and the dual formulation for X3. X3 is the group coding matrix associated
# with the qualitative variable Loc. This block is considered
# as response block and specified using the argument response.
fit_rgcca < rgcca(
blocks = blocks,
response = 3,
method = "rgcca",
tau = c(1, 1, 0),
ncomp = 1,
scheme = function(x) x^2, #factorial scheme,
verbose = TRUE,
)
fit_rgcca$primal_dual
print(fit_rgcca)
###########################################
# Example 6: RGCCA and variable selection #
###########################################
# Variable selection and RGCCA : the sgcca algorithm
fit_sgcca < rgcca(
blocks = blocks,
method = "sgcca",
response = 3,
sparsity = c(.071, .2, 1), ncomp = 1,
scheme = "factorial", verbose = TRUE,
)
print(fit_sgcca)
############################################
# Example 7: RGCCA, multiple components #
# and different penalties per component #
############################################
# S/RGCCA algorithm with multiple components and different
# penalties for each components (> sparsity is a matrix)
fit_rgcca < rgcca(blocks, response = 3,
tau = matrix(c(.5, .5, 0, 1, 1, 0), nrow = 2, byrow = TRUE),
ncomp = c(2, 2, 1), scheme = "factorial")
print(fit_rgcca)
# the same applies for SGCCA
fit_sgcca < rgcca(blocks, response = 3,
sparsity = matrix(c(.071, 0.2, 1,
0.06, 0.15, 1), nrow = 2, byrow = TRUE),
ncomp = c(2, 2, 1), scheme = "factorial")
print(fit_sgcca)
##################################################
# Example 8: Supervised mode en cross validation #
##################################################
# Prediction of the location from GE and CGH
# Tune sparsity values based on the crossvalidated accuracy.
set.seed(27) #favorite number
cv_out < rgcca_cv(blocks, response = 3,
par_type = "sparsity",
par_length = 10,
ncomp = 1,
prediction_model = "lda",
metric = "Accuracy",
k = 3, n_run = 5,
n_cores = 2)
print(cv_out)
plot(cv_out, display_order = TRUE)
# all the parameters were imported from the fitted cval object.
fit_rgcca < rgcca(cv_out)
print(fit_rgcca)
## End(Not run)
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