wrap.correlation: Prepare Data on Correlation Manifold In Riemann: Learning with Data on Riemannian Manifolds

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

 1 wrap.correlation(input)

Arguments

 input correlation data matrices to be wrapped as riemdata class. Following inputs are considered, arrayan (p\times p\times n) array where each slice along 3rd dimension is a correlation matrix. lista 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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 #------------------------------------------------------------------- # 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)

Riemann documentation built on June 20, 2021, 5:07 p.m.