- blocks
A list that contains the \(J\) blocks of variables
\(\mathbf{X_1}, \mathbf{X_2}, ..., \mathbf{X_J}\).
Block \(\mathbf{X}_j\) is a matrix of dimension
\(n \times p_j\) where \(n\) is the number of
observations and \(p_j\) the number of variables. The blocks argument can
be also a fitted cval, rgcca or permutation object.
- method
A string specifying which multiblock component
method to consider. Possible values are found using
available_methods.
- response
A numerical value giving the position of the response block.
When the response argument is filled, the supervised mode is automatically
activated.
- par_type
A character giving the parameter to tune among "sparsity",
"tau" or "ncomp".
- par_value
The parameter values to be tested, either NULL,
a numerical vector of size \(J\), or a matrix of size
par_length \(\times J\).
If par_value is NULL, up to par_length sets of parameters are generated
uniformly from
the minimum and maximum possible values of the parameter defined by par_type
for each block. Minimum possible values are 0 for tau,
\(1/\textrm{sqrt}(p_j)\) for sparsity, and 1
for ncomp. Maximum possible values are 1 for tau and sparsity, and
\(p_j\) for ncomp.
If par_value is a vector, it overwrites the maximum values taken for the
range of generated parameters.
If par_value is a matrix, par_value directly corresponds to the set of
tested parameters.
- par_length
An integer indicating the number of sets of candidate
parameters to be tested (if par_value is not a matrix).
- validation
A string specifying the type of validation among "loo" and
"kfold". For small datasets (e.g. <30 samples), it is recommended to use a
loo (leave-one-out) procedure.
- prediction_model
A string giving the model used for prediction.
Please see caret::modelLookup() for a list of the available models.
- metric
A string indicating the metric of interest.
It should be one of the following scores:
For classification: "Accuracy", "Kappa", "F1", "Sensitivity", "Specificity",
"Pos_Pred_Value", "Neg_Pred_Value", "Precision", "Recall", "Detection_Rate",
"Balanced_Accuracy".
For regression: "RMSE", "MAE".
- k
An integer giving the number of folds (if validation = 'kfold').
- n_run
An integer giving the number of Monte-Carlo Cross-Validation
(MCCV) to be run (if validation = 'kfold').
- n_cores
The number of cores used for parallelization.
- quiet
A logical value indicating if some diagnostic messages
are reported.
- superblock
A logical value indicating if the
superblock option is used.
- scale
A logical value indicating if variables are standardized.
- 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.
- tol
The stopping value for the convergence of the algorithm
(default: tol = 1e-08).
- 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.
- NA_method
A string indicating the method used for
handling missing values ("na.ignore", "na.omit"). (default: "na.ignore").
"na.omit" corresponds to perform RGCCA on the fully observed
observations (observations from which missing values have been removed).
"na.ignore" corresponds to perform RGCCA algorithm on available
data (See Tenenhaus et al, 2005).
- rgcca_res
A fitted RGCCA object (see rgcca).
- tau
Either a numerical value, a numeric vector of size
\(J\), or a
numeric matrix of dimension
\(\mathrm{max}(\textrm{ncomp}) \times J\)
containing the values of the regularization parameters
(default: tau = 1, for each
block and each dimension), or a string equal to "optimal".
The regularization parameters varies from 0 (maximizing the correlation) to
1 (maximizing the covariance).
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 \(\mathbf X_j\).
If tau is a matrix, tau[k, j] is associated with the constraints
applied to the kth block weight vector corresponding to block
\(\mathbf X_j\).
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 \(J\) indicating
the number of components per block. If a single value is provided,
the same number of components is extracted for every block.
- sparsity
Either a numerical value, a numeric vector of
size \(J\) or a numeric matrix
of dimension \(\textrm{max}(\textrm{ncomp}) \times J\) encoding the L1
constraints applied to the
block weight vectors. For block \(j\), the amount of
sparsity varies between
\(1/\textrm{sqrt}(p_j)\) and 1 (larger values of sparsity
correspond to less penalization).
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
\(\mathbf X_j\):
$$
\forall k, \Vert a_{j,k} \Vert_{1} \le \textrm{sparsity}[j] \sqrt{p_j}.
$$
If sparsity is a matrix, sparsity[k, j] is associated with the constraints
applied to the kth block weight vector corresponding to block
\(\mathbf X_j\):
$$
\Vert a_{j,k}\Vert_{1} \le \textrm{sparsity}[k,j] \sqrt{p_j}.
$$
The sparsity parameter can be estimated by using rgcca_permutation or
rgcca_cv.
- 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 (\(1/n\)) or unbiased
(\(1/(n-1)\)) estimator of the variance/covariance
(default: bias = TRUE).
- verbose
A logical value indicating if the progress of the
algorithm is reported while computing.
- 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.
- ...
Additional parameters to be passed to prediction_model.