View source: R/Final_functions.R

RobMM | R Documentation |

Robust Mixture Model

```
RobMM(X, nclust=2:5, model="Gaussian", ninit=10,
nitermax=50, niterEM=50, niterMC=50, df=3,
epsvp=10^(-4), mc_sample_size=1000, LogLike=-Inf,
init='genie', epsPi=10^-4, epsout=-20,scale='none',
alpha=0.75, c=ncol(X), w=2, epsilon=10^(-8),
criterion='BIC',methodMC="RobbinsMC", par=TRUE,
methodMCM="Weiszfeld")
```

`X` |
A matrix giving the data. |

`nclust` |
A vector of positive integers giving the possible number of clusters. |

`model` |
The mixture model. Can be |

`ninit` |
The number of random initisalizations. Befault is |

`nitermax` |
The number of iterations for the Weiszfeld algorithm if |

`niterEM` |
The number of iterations for the EM algorithm. |

`niterMC` |
The number of iterations for estimating robustly the variance of each class if |

`df` |
The degrees of freedom for the Student law if |

`scale` |
Run the algorithm on scaled data if |

`epsvp` |
The minimum values the estimates of the eigenvalues of the Median Covariation Matrix can take. Default is |

`mc_sample_size` |
The number of data generated for the Monte-Carlo method for estimating robustly the variance. |

`LogLike` |
The initial loglikelihood to "beat". Defulat is |

`init` |
Can be |

`epsPi` |
A scalar to ensure the estimates of the probabilities of belonging to a class or uniformly lower bounded by a positive constant. |

`epsout` |
If the probability of belonging of a data to a class is smaller than |

`alpha` |
A scalar between 1/2 and 1 used in the stepsequence for the Robbins-Monro method if |

`c` |
The constant in the stepsequence if |

`w` |
The power for the weighted averaged Robbins-Monro algorithm if |

`epsilon` |
Stoping condition for the Weiszfeld algorithm. |

`criterion` |
The criterion for selecting the number of cluster. Can be |

`methodMC` |
The method chosen to estimate robustly the variance. Can be |

`par` |
Is equal to |

`methodMCM` |
The method chosen for estimating the Median Covariation Matrix. Can be |

A list with:

`bestresult` |
A list giving all the results fo the best clustering (chosen with respect to the selected criterion. |

`allresults` |
A list containing all the results. |

`ICL` |
The ICL criterion for all the number of classes selected. |

`BIC` |
The ICL criterion for all the number of classes selected. |

`data` |
The initial data. |

`nclust` |
A vector of positive integers giving the possible number of clusters. |

`Kopt` |
The number of clusters chosen by the selected criterion. |

For the lists `bestresult`

and `allresults[[k]]`

:

`centers` |
A matrix whose rows are the centers of the classes. |

`Sigma` |
A matrix containing all the variance of the classes |

`LogLike` |
The final LogLikelihood. |

`Pi` |
A matrix giving the probabilities of each data to belong to each class. |

`niter` |
The number of iterations of the EM algorithm. |

`initEM` |
A vector giving the initialized clustering if |

`prop` |
A vector giving the proportions of each classes. |

`outliers` |
A vector giving the detected outliers. |

Cardot, H., Cenac, P. and Zitt, P-A. (2013). Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. *Bernoulli*, 19, 18-43.

Cardot, H. and Godichon-Baggioni, A. (2017). Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis. *Test*, 26(3), 461-480

Vardi, Y. and Zhang, C.-H. (2000). The multivariate L1-median and associated data depth. *Proc. Natl. Acad. Sci. USA*, 97(4):1423-1426.

See also `Gen_MM`

, `RMMplot`

and `RobVar`

.

```
## Not run:
ech <- Gen_MM(mu = matrix(c(rep(-2,3),rep(2,3),rep(0,3)),byrow = TRUE,nrow=3))
X <- ech$X
res <- RobMM(X , nclust=3)
RMMplot(res,graph=c('Two_Dim'))
## End(Not run)
```

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