# Finite mixture modeling and model-based clustering based on Manly mixture models.

### Description

The utility of this package includes finite mixture modeling and model-based clustering based on Manly mixtures as well as forward and backward model selection procedures.

### Details

Package: | ManlyMix |

Type: | Package |

Version: | 0.1.7 |

Date: | 2016-12-01 |

License: | GPL (>= 2) |

LazyLoad: | no |

Function 'Manly.sim' simulates Manly mixture datasets.

Function 'Manly.overlap' estimates the pairwise overlaps for a Manly mixture.

Function 'Manly.EM' runs the EM algorithm for Manly mixture models.

Function 'Manly.select' runs forward and backward model selection procedures.

Function 'Manly.CEM' runs k-means model with Manly transformation.

Function 'Manly.var' produces the variance-covariance matrix of the parameter estimates from Manly mixture model.

Function 'Manly.contour' produces the contour plot of Manly mixture.

### Author(s)

Xuwen Zhu and Volodymyr Melnykov.

Maintainer: Xuwen Zhu <xuwen.zhu@louisville.edu>

### References

Zhu, X. and Melnykov, V. (2016) “Manly Transformation in Finite Mixture Modeling”, *Journal of Computational Statistics and Data Analysis*, doi:10.1016/j.csda.2016.01.015.

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 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
set.seed(123)
K <- 3; p <- 4
X <- as.matrix(iris[,-5])
id.true <- rep(1:K, each = 50)
# Obtain initial memberships based on the K-means algorithm
id.km <- kmeans(X, K)$cluster
# Run the CEM algorithm for Manly K-means model
la <- matrix(0.1, K, p)
C <- Manly.Kmeans(X, id = id.km, la = la)
# Run the EM algorithm for a Gaussian mixture model based on K-means solution
G <- Manly.EM(X, id = id.km)
id.G <- G$id
# Run FORWARD SELECTION ('silent' is on)
F <- Manly.select(X, model = G, method = "forward", silent = TRUE)
# Run the EM algorithm for a full Manly mixture model based on Gaussian mixture solution
la <- matrix(0.1, K, p)
M <- Manly.EM(X, id = id.G, la = la)
# Run BACKWARD SELECTION ('silent' is off)
B <- Manly.select(X, model = M, method = "backward")
BICs <- c(G$bic, M$bic, F$bic, B$bic)
names(BICs) <- c("Gaussian", "Manly", "Forward", "Backward")
BICs
``` |