overlapGOM {MixSim}

Generalized overlap of Maitra

Description

Computes the generalized overlap as defined by R. Maitra.

Usage

overlapGOM(Pi, Mu, S, eps = 1e-06, lim = 1e06)

Arguments

Pi

vector of mixing proprtions (length K).

Mu

matrix consisting of components' mean vectors (K * p).

S

set of components' covariance matrices (p * p * K).

eps

error bound for overlap computation.

lim

maximum number of integration terms (Davies, 1980).

Value

Returns the value of goMega.

Author(s)

Volodymyr Melnykov, Wei-Chen Chen, and Ranjan Maitra.

References

Maitra, R. (2010) “A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps”, NeuroImage, 50, 124-135.

Melnykov, V., Chen, W.-C., and Maitra, R. (2012) “MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms”, Journal of Statistical Software, 51:12, 1-25.

Davies, R. (1980) “The distribution of a linear combination of chi-square random variables”, Applied Statistics, 29, 323-333.

See Also

MixSim, MixGOM, and overlap.

Examples

data("iris", package = "datasets")
p <- ncol(iris) - 1
id <- as.integer(iris[, 5])
K <- max(id)

# estimate mixture parameters
Pi <- prop.table(tabulate(id))
Mu <- t(sapply(1:K, function(k){ colMeans(iris[id == k, -5]) }))
S <- sapply(1:K, function(k){ var(iris[id == k, -5]) })
dim(S) <- c(p, p, K)

overlapGOM(Pi = Pi, Mu = Mu, S = S)