Description Usage Arguments Details Value References See Also Examples

This function estimates the model-based clustering which is under the framework of finite mixture models.

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`K` |
A vector of the number of clusters |

`y` |
A p-dimensional data matrix. Each row is an observation |

`N` |
The maximum number of iterations in the EM algorithm. The default value is 100. |

`kms.iter` |
The maximum number of iterations in the K-means algorithm whose outputs are the starting values for the EM algorithm |

`kms.nstart` |
The number of starting values in K-means |

`eps.diff` |
The lower bound of pairwise difference of two mean values. Any value lower than it is treated as 0 |

`eps.em` |
The lower bound for the stopping criterion. |

`model.crit` |
The criterion used to select the number of clusters |

`short.output` |
A short version of output is needed or not. A short version is used for computing the adaptive parameters in APFP or APL1 methods. The default value is FALSE. |

This function estimates parameters *μ*, *Σ*, *π* and the clustering assignments in the model-based clustering using the mixture model,

*y \sim ∑_{k=1}^K π_k f(y|μ_k, Σ)*

where *f(y|μ_k, Σ_k)* is the density function of Normal distribution with mean *μ_k* and variance *Σ*. Here we assume that each cluster has the same diagonal variance.

This function is also used to compute the adaptive parameters for functions `apfp`

and `apL1`

.

This function returns the esimated parameters and some statistics of the optimal model within the given *K* and *λ*, which is selected by BIC when `model.crit = 'bic'`

or GIC when `model.crit = 'gic'`

.

`mu.hat.best` |
The estimated cluster means. |

`sigma.hat.best` |
The estimated covariance. |

`p.hat.best` |
The estimated cluster proportions. |

`s.hat.best` |
The clustering assignments. |

`K.best` |
The value of |

`llh.best` |
The log-likelihood of the optimal model |

`gic.best` |
The GIC of the optimal model |

`bic.best` |
The BIC of the optimal model |

`ct.mu.best` |
The degrees of freedom in the cluster means of the optimal model |

Fraley, C., & Raftery, A. E. (2002) Model-based clustering, discriminant analysis, and density estimation. *Journal of the American statistical Association* **97(458)**, 611–631.

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