Manly.overlap {ManlyMix}

Estimates the overlap for a Manly mixture

Description

Estimates the pairwise overlap matrix for a Manly mixture by simulating samples based on user-specified parameters.

Usage

Manly.overlap(tau, Mu, S, la, N = 1000)

Arguments

la

matrix of transformation parameters (K x p)

tau

vector of mixing proportions (length K)

Mu

matrix of mean vectors (K x p)

S

array of covariance matrices (p x p x K)

N

number of samples simulated

Details

Estimates the pairwise overlap matrix for a Manly mixture. Overlap is defined as sum of two misclassification probabilities.

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 overlap.

MaxOmega

value of maximum overlap.

References

Maitra, R. and Melnykov, V. (2010) “Simulating data to study performance of finite mixture modeling and clustering algorithms”, 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.

Examples

set.seed(123)
#sets the number of components, dimensionality and sample size
K <- 3
p <- 2

#sets the mixture parameters
tau <- c(0.25, 0.3, 0.45)
Mu <- matrix(c(4.5,4,5,7,8,5.5),3)
la <- matrix(c(0.2,0.5,0.3,0.25,0.35,0.4),3)
S <- array(NA, dim = c(p,p,K))
S[,,1] <- matrix(c(0.4,0,0,0.4),2)
S[,,2] <- matrix(c(1,-0.2,-0.2,0.6),2)
S[,,3] <- matrix(c(2,-1,-1,2),2)

#computes the overlap
A <- Manly.overlap(tau, Mu, S, la)
print(A)