CovMean {CovTools}

Estimate Mean Covariance Matrix

Description

For a given 3-dimensional array where symmetric positive definite (SPD) matrices are stacked slice by slice, it estimates Frechet mean on an open cone of SPD matrices under corresponding metric/distance measure.

Usage

CovMean(
  A,
  method = c("AIRM", "Cholesky", "Euclidean", "LERM", "Procrustes.SS",
    "Procrustes.Full", "PowerEuclidean", "RootEuclidean"),
  power = 1
)

Arguments

A

a (p\times p\times N) 3d array of N SPD matrices.

method

the type of distance measures to be used; "AIRM" for Affine Invariant Riemannian Metric, "Cholesky" for Cholesky difference in Frobenius norm, "Euclidean" for naive Frobenius norm as distance, "LERM" for Log Euclidean Riemannian Metric, "Procrustes.SS" for Procrustes Size and Shape measure, "Procrustes.Full" for Procrustes analysis with scale, "PowerEuclidean" for weighted eigenvalues by some exponent, and "RootEuclidean" for matrix square root.

power

a non-zero number for PowerEuclidean distance.

Value

a (p\times p) mean covariance matrix estimated.

References

Dryden IL, Koloydenko A, Zhou D (2009). “Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging.” The Annals of Applied Statistics, 3(3), 1102–1123. ISSN 1932-6157.

Examples

## Not run: 
## generate 100 sample covariances of size (5-by-5).
pdim    = 5
samples = samplecovs(100,pdim)

## compute mean of first 50 sample covariances from data under Normal(0,Identity).
mLERM = CovMean(samples[,,1:50], method="LERM")
mAIRM = CovMean(samples[,,1:50], method="AIRM")
mChol = CovMean(samples[,,1:50], method="Cholesky")
mRoot = CovMean(samples[,,1:50], method="RootEuclidean")

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(mLERM[,pdim:1], main="LERM mean")
image(mAIRM[,pdim:1], main="AIRM mean")
image(mChol[,pdim:1], main="Cholesky mean")
image(mRoot[,pdim:1], main="RootEuclidean mean")
par(opar)

## End(Not run)