rgccak: Internal function for computing the RGCCA parameters (RGCCA...
In ecamenen/r-rgcca: RGCCA and Sparse GCCA for multi-block data analysis

Description Usage Arguments Value References

The function rgccak() is called by rgcca() and does not have to be used by the user. The function rgccak() computes the RGCCA block components, outer weight vectors, etc., for each block and each dimension. Depending on the dimensionality of each block \mathbf{X}_j , j = 1, …, J, the primal (when n > p_j) or the dual (when n < p_j) algorithm is used (see Tenenhaus et al. 2013)

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  rgccak(A, C, tau = "optimal", scheme = "centroid",
    scale = FALSE, verbose = FALSE, init = "svd",
    bias = TRUE, tol = .Machine$double.eps)

`A`	A list that contains the J blocks of variables. Either the blocks (\mathbf{X}_1, \mathbf{X}_2, …, \mathbf{X}_J) or the residual matrices (\mathbf{X}_{h1}, \mathbf{X}_{h2}, …, \mathbf{X}_{hJ}).
`C`	A design matrix that describes the relationships between blocks. (Default: complete design).
`tau`	A 1 \times J vector that contains the values of the shrinkage parameters τ_j, j=1, … J. (Default: τ_j = 1, j=1, …, J). If tau = "optimal" the shrinkage intensity paramaters are estimated using the Schafer and Strimmer (2005) analytical formula.
`scheme`	Either "horst", "factorial" or "centroid" (default: centroid).
`scale`	if scale = TRUE, each block is standardized to zero means and unit variances (default: TRUE).
`verbose`	Will report progress while computing if verbose = TRUE (default: TRUE).
`init`	The mode of initialization to use in the RGCCA algorithm. The alternatives are either by Singular Value Decompostion or random (default : "svd").
`bias`	A logical value for either a biaised or unbiaised estimator of the var/cov.
`tol`	Stopping value for convergence.

`Y`	A n \times J matrix of RGCCA outer components
`Z`	A n \times J matrix of RGCCA inner components
`a`	A list of outer weight vectors
`crit`	The values of the objective function to be optimized in each iteration of the iterative procedure.
`converg`	Speed of convergence of the algorithm to reach the tolerance.
`AVE`	Indicators of model quality based on the Average Variance Explained (AVE): AVE(for one block), AVE(outer model), AVE(inner model).
`C`	A design matrix that describes the relationships between blocks (user specified).
`tau`	1 \times J vector containing the value for the tau penalties applied to each of the J blocks of data (user specified)
`scheme`	The scheme chosen by the user (user specified).

Tenenhaus A. and Tenenhaus M., (2011), Regularized Generalized Canonical Correlation Analysis, Psychometrika, Vol. 76, Nr 2, pp 257-284.

Tenenhaus A. et al., (2013), Kernel Generalized Canonical Correlation Analysis, submitted.

Schafer J. and Strimmer K., (2005), A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32.

ecamenen/r-rgcca documentation built on Jan. 16, 2020, 12:50 a.m.