regCCA: Generalized Canonical Correlation Analysis
In dmt: Dependency Modeling Toolkit

Description Usage Arguments Details Value Author(s) References See Also Examples

Solve generalized CCA. Contains a possibility to regularize the solution to reduce the effect of noise.

1	regCCA(datasets, reg=0)

datasets

A list containing the data matrices to be analyzed. Each matrix needs to have the same number of rows (samples), but the number of columns (features) can differ. Each row needs to correspond to the same sample in every matrix.

reg

Regularization parameter for the whitening step used to remove data-set specific variation. The value of parameter must be between 0 and 1. The default value is set to 0, which means no regularization will be used. If a non-zero value is given it means that some of the dimensions with the lowest variance are ignored when whitening. In more terms, the dimensions whose total contribution to sum of eigenvalues of the covariance matrix of each data set is below reg will not be used for the whitening.

The function implements generalized CCA by explicitly whitening the data sets and then performing a principal component analysis on the collection of whitened data sets, instead of directly solving the generalized eigenproblem. Singular value decomposition is used for both the whitening and the PCA phase, and row-wise mean values of each data set are removed before whitening.

The function returns a list with following components

`eigval`	Generalized canonical correlations. In case of two data sets (eigval-1) would give the correlations.
`eigvecs`	List of projection matrices, one for each data set. Each projection matrix is a N times m matrix where N is the number of samples and m is the total number of dimensions in all of the data sets.
`proj`	Projection of the original data sets by the corresponding projection matrices.
`meanvec`	An array containing columnwise mean vectors for each data matrix
`white`	An array of whitening matrices for each data set. This might not be of user interest but this value is used as input in other functions in the package.

The function also prints whether regularization was used or not.

Abhishek Tripathi abhishektripathi.at@gmail.com, Arto Klami

Hotelling H. (1936), Relations between two sets of variables, Biometrika, 28, 321-327.

Kettenring J.R. (1971), Canonical Analysis of several sets of variables, Biometrika, 58:3, 433-451.

Tripathi A., Klami A., Kaski S. (2007), Simple integrative preprocessing preserves what is shared in data sources.

cancor,prcomp,svd

#     data(expdata1)
#     data(expdata2)

     #performing regCCA
#    test <- regCCA(list(expdata1,expdata2),0) #list of result is stored in test
 
#     test$eigval #generalized canonical correlations
#     test$eigvecs #gCCA components
#     test$proj #projection of data onto gCCA components
#     test$meanvec #array of columnwise mean vectors for each matrix
#     test$white # array of whitening matrix