overlap {MixSim}R Documentation

Overlap

Description

Computes misclassification probabilities and pairwise overlaps for finite mixture models with Gaussian components. Overlap is defined as sum of two misclassification probabilities

Usage

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

Arguments

Pi vector of mixing proprtions (length K)
Mu matrix consisting of components' mean vectors (K x p)
S set of components' covariance matrices (p x p x K)
eps error bound for overlap computation
acc error bound for integration (Davies, 1980)
lim maximum number of integration terms (Davies, 1980)

Value

OmegaMap matrix of misclassification probabilities (K x K); OmegaMap[i,j] is the probability that X coming from the i-th component is classified to the j-th component
BarOmega value of average overap
MaxOmega value of maximum overap
rcMax row and column numbers for the pair of components producing maximum overlap 'MaxOmega'

Author(s)

Melnykov, V., Chen, W.-C., Maitra, R.

References

Maitra, R. and Melnykov, V. (200?) "Simulating data to study performance of finite mixture modeling and clustering algorithms", The Journal of Computational and Graphical Statistics.

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

See Also

MixSim, pdplot, simdataset

Examples

data(iris)

p <- dim(iris)[2] - 1
n <- dim(iris)[1]
K <- 3

id <- as.numeric(iris[,5])
Pi <- NULL
Mu <- NULL
S <- array(rep(0, p * p * K), c(p, p, K))

# estimate mixture parameters
for (k in 1:K){
        Pi <- c(Pi, sum(id == k) / n)
        Mu <- rbind(Mu, apply(iris[id == k,-5], 2, mean))
        S[,,k] <- var(iris[id == k,-5])
}

overlap(Pi = Pi, Mu = Mu, S = S)

[Package MixSim version 0.1-04 Index]