# Manly.overlap: Estimates the overlap for a Manly mixture In ManlyMix: Manly Mixture Modeling and Model-Based Clustering

## Description

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

## Usage

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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 26, 2018, 1:04 a.m.