frcc {FRCC}

This function implements the Fast Regularized Canonical Correlation Analysis

Description

This function implements the Fast Regularized Canonical Correlation algorithm described in [Cruz-Cano et al., 2014].

The main idea of the algorithm is using the minimum risk estimators of the correlation matrices described in [Schafer and Strimmer, 2008] during the calculation of the Canonical correlation Structure.

It can be considered an extension of the work for two set of variables (blocks) mentioned in [Tenenhaus and Tenenhaus, 2011].

Usage

frcc(X, Y)

Arguments

X

numeric matrix (n by p) which contains the observations on the X variables.

Y

numeric matrix (n by q) which contains the observations on the Y variables.

Value

A list with the following components of the Canonical Structure:

cor

Canonical correlations.

p_values

The corresponding p-values for the each of the canonical correlations.

canonical_weights_X

The canonical weights for the variables of the dataset X.

canonical_weights_Y

The canonical weights for the variables of the dataset Y.

canonical_factor_loadings_X

The inter-set canonical factor loadings for the variables of the dataset X.

canonical_factor_loadings_Y

The inter-set canonical factor loadings for the variables of the dataset Y.

Author(s)

Raul Cruz-Cano

References

Cruz-Cano, R.; Lee, M.L.T.; Fast Regularized Canonical Correlation Analysis, Computational Statistics & Data Analysis, Volume 70, 2014, Pages 88-100, ISSN 0167-9473, https://doi.org/10.1016/j.csda.2013.09.020.

Schafer, J; Strimmer, K. (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology 4:14, Article 32.

Tenenhaus, A.; Tenenhaus, M. (2011). Regularized Generalized Canonical Correlation Analysis. Psychometrika 76:2, DOI: 10.1007/S11336-011-9206-8.

Examples

# Example # 1 Multivariate Normal Data
p<-10
q<-10
n<-50
res<-generate_multivariate_normal_sample(p,q,n)
X<-res$X
Y<-res$Y
rownames(X)<-c(1:n)
colnames(X)<-c(1:p)
colnames(Y)<- c(1:q)
my_res<-frcc(X,Y)
print(my_res)
#Example #2 Soil Specification Data
data(soilspec)
list_of_units_to_be_used<-sample(1:nrow(soilspec),14)
X<- soilspec[list_of_units_to_be_used,2:9]
Y<- soilspec[list_of_units_to_be_used,10:15]
colnames(X)<-c("H. pubescens", "P. bertolonii", "T. pretense",
               "P. sanguisorba", "R. squarrosus", "H. pilosella", "B. media","T. drucei")
colnames(Y)<- c("d","P","K","d x P", "d x K","P x K")
my_res<-frcc(X,Y)
grDevices::dev.new()
plot_variables(my_res,1,2)
#Example #3 NCI-60 micrRNA Data
data("Topoisomerase_II_Inhibitors")
data("microRNA")
my_res <- frcc(t(microRNA),-1*t(Topoisomerase_II_Inhibitors))
for( i in 1:dim(microRNA)[2])
{
  colnames(microRNA)[i]<-substr(colnames(microRNA)[i], 1, 2)
}#end for i