overlap {MixSim}

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 * 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

OmegaMap

matrix of misclassification probabilities (K * 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 overlap.

MaxOmega

value of maximum overlap.

rcMax

row and column numbers for the pair of components producing maximum overlap 'MaxOmega'.

Author(s)

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

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.

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, pdplot, and simdataset.

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)

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