ridgeline {fpc}

Ridgeline computation

Description

Computes (\alpha*\Sigma_1^{-1}+(1-\alpha)*\Sigma_2^{-1})^{-1}* \alpha*(\Sigma_1^{-1}*\mu_1)+(1-\alpha)*(\Sigma_2^{-1}*\mu_2) as required for the computation of the ridgeline (Ray and Lindsay, 2005) to find all density extrema of a two-component Gaussian mixture with mean vectors mu1 and mu2 and covariance matrices Sigma1, Sigma2.

Usage

ridgeline(alpha, mu1, mu2, Sigma1, Sigma2)

Arguments

alpha

numeric between 0 and 1.

mu1

mean vector of component 1.

mu2

mean vector of component 2.

Sigma1

covariance matrix of component 1.

Sigma2

covariance matrix of component 2.

Value

A vector. See above.

Author(s)

Christian Hennig [e-mail] https://www.unibo.it/sitoweb/christian.hennig/en/

References

Ray, S. and Lindsay, B. G. (2005) The Topography of Multivariate Normal Mixtures, Annals of Statistics, 33, 2042-2065.

Examples

  ridgeline(0.5,c(1,1),c(2,5),diag(2),diag(2))