variationKernel: Compute the variation kernel

In DistributionalDDA: Distributional Data Analysis in Bayes Spaces

Compute the variation kernel

Description

Variance in Bayes spaces can be expressed in various forms. The variation kernel is essentially the variance of the difference of the log-densities or clr-transforms at evaluated at different values

Usage

variationKernel(X, ...)

## S3 method for class 'BDataSplines'
variationKernel(X, ...)

## S3 method for class 'BData'
variationKernel(X, ...)

## S3 method for class ''function''
variationKernel(X, basis = getBayesSpaceBasis(X), ...)

## S3 method for class 'variationKernel'
variationKernel(X, basis = getBayesSpaceBasis(X), ...)

Arguments

X	a dataset of BData objects
...	further parameters detailing computation
basis	the BayesSpaceBasis for which this covariance kernel is valid

Details

v(x) = (var( clr(X)(x_i) - clr(X)(y_j)))_ij

It relates to the covariance like the variogram of the residual mean corrected field corresponds to the covariance. The advantage of the variation kernel is its subcompositional coherence, i.e. it is independent of support and reference measure.

Value

a function of two arguments with a basis attribute representing the BayesSpaceBasis, and variationKernel class.

Methods (by class)

• variationKernel(BDataSplines): method for BDataSplines uses the covariance of the spline coefficients to compute

• variationKernel(BData): default method for BData computes implicitly using clr transforms.

• variationKernel(`function`): constructor

• variationKernel(variationKernel): method for varKernel, keeps the kernel, possibly overwrites the basis.

See Also

plot.variationKernel, varKernel

Examples

data(DTD)
X = BDataPDFs(DTD$shapePDF,basis=B2Unif01Basis5)
V = variationKernel(X)
V
plot(V)

K = BDataSplines(matrix(rnorm(10*5),ncol=5),basis=B2Unif01Basis5)
V2 = variationKernel(K)
V2
plot(V2)

DistributionalDDA documentation built on Oct. 20, 2026, 5:06 p.m.