# EM Algorithm for GMM

### Description

Expectation-Maximization algorithm to calculate optimal Gaussian Mixture Model for given data in one Dimension.

### Usage

1 | ```
EMGauss(Data, Means, SDs,Weights, MaxNumberofIterations,fast)
``` |

### Arguments

`Data` |
vector of data points |

`Means` |
vector(1:L), Means of Gaussians, L == Number of Gaussians |

`SDs` |
estimated Gaussian Kernels = standard deviations |

`Weights` |
optional, relative number of points in Gaussians (prior probabilities): sum(Weights) ==1, default weight is 1/L |

`MaxNumberofIterations` |
Optional, Number of Iterations; default=10 |

`fast` |
Default: FALSE: Using mclust's EM see function |

### Details

No adding or removing of Gaussian kernels. Number of Gaussian hast to be set by the length of the vector of Means, SDs and Weights.
This EM is only for univariate data. For multivariate data see package `mclust`

### Value

List with

`Means` |
means of GMM generated by EM algorithm |

`SDs` |
standard deviations of GMM generated by EM algorithm |

`Weights` |
prior probabilities of Gaussians |

### Author(s)

Onno Hansen-Goos, Michael Thrun

### References

Bishop, Christopher M. Pattern recognition and machine learning. springer, 2006, p 435 ff

### See Also

`AdaptGauss`