MixSim (version 1.0-2)

overlap: 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, 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

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'

References

Maitra, R. and Melnykov, V. (2010) "Simulating data to study performance of finite mixture modeling and clustering algorithms", The Journal of Computational and Graphical Statistics, 2:19, 354-376.

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)