Manly.overlap: Estimates the overlap for a Manly mixture

In ManlyMix: Manly Mixture Modeling and Model-Based Clustering

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)

ManlyMix documentation built on April 29, 2023, 9:17 a.m.