wrap.correlation {Riemann}

Prepare Data on Correlation Manifold

Description

The collection of correlation matrices is considered as a subset (and quotient) of the well-known SPD manifold. In our package, it is defined as

\mathcal{C}_{++}^p = \lbrace X \in \mathbf{R}^{p\times p} ~\vert~ X^\top = X,~ \textrm{rank}(X)=p,~ \textrm{diag}(X) = 1 \rbrace

where the rank condition means it is strictly positive definite. Please note that the geometry involving semi-definite correlation matrices is not the objective here.

Usage

wrap.correlation(input)

Arguments

input

correlation data matrices to be wrapped as riemdata class. Following inputs are considered,

array

an (p\times p\times n) array where each slice along 3rd dimension is a correlation matrix.

list

a length-n list whose elements are (p\times p) correlation matrices.

Value

a named riemdata S3 object containing

data

a list of (p\times p) correlation matrices.

size

size of each correlation matrix.

name

name of the manifold of interests, "correlation"

Examples

#-------------------------------------------------------------------
#                 Checker for Two Types of Inputs
#
#  5 observations; empirical correlation of normal observations.
#-------------------------------------------------------------------
#  Data Generation
d1 = array(0,c(3,3,5))
d2 = list()
for (i in 1:5){
  dat = matrix(rnorm(10*3),ncol=3)
  d1[,,i] = stats::cor(dat)
  d2[[i]] = d1[,,i]
}

#  Run
test1 = wrap.correlation(d1)
test2 = wrap.correlation(d2)