ManlyMix (version 0.1.15.1)

Manly.overlap: 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)

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.

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.

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)