AdaptGauss-package {AdaptGauss} | R Documentation |

## Gaussian Mixture Models (GMM)

### Description

Multimodal distributions can be modelled as a mixture of components. The model is derived using the Pareto Density Estimation (PDE) for an estimation of the pdf. PDE has been designed in particular to identify groups/classes in a dataset. Precise limits for the classes can be calculated using the theorem of Bayes. Verification of the model is possible by QQ plot, Chi-squared test and Kolmogorov-Smirnov test. The package is based on the publication of Ultsch, A., Thrun, M.C., Hansen-Goos, O., Lotsch, J. (2015) <DOI:10.3390/ijms161025897>.

### Details

Multimodal distributions can be modelled as a mixture of components. The model is derived using the Pareto Density Estimation (PDE) for an estimation of the pdf [Ultsch 2005]. PDE has been designed in particular to identify groups/classes in a dataset. The expectation maximization algorithm estimates a Gaussian mixture model of density states [Bishop 2006] and the limits between the different states are defined by Bayes decision boundaries [Duda 2001]. The model can be verified with Chi-squared test, Kolmogorov-Smirnov test and QQ plot.

The correct number of modes may be found with AIC or BIC.

Index: This package was not yet installed at build time.

### Author(s)

Michael Thrun, Onno Hansen-Goos, Rabea Griese, Catharina Lippmann, Florian Lerch, Jorn Lotsch, Alfred Ultsch Maintainer: Michael Thrun <m.thrun@gmx.net>

### References

Ultsch, A., Thrun, M.C., Hansen-Goos, O., Loetsch, J.: Identification of Molecular Fingerprints in Human Heat Pain Thresholds by Use of an Interactive Mixture Model R Toolbox(AdaptGauss), International Journal of Molecular Sciences, doi:10.3390/ijms161025897, 2015.

Duda, R.O., P.E. Hart, and D.G. Stork, Pattern classification. 2nd. Edition. New York, 2001, p 512 ff

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

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

Thrun M.C., Ultsch, A.: Models of Income Distributions for Knowledge Discovery, European Conference on Data Analysis, DOI 10.13140/RG.2.1.4463.0244, Colchester 2015.

### Examples

```
## Statistically significant GMM
## Not run:
data=c(rnorm(3000,2,1),rnorm(3000,7,3),rnorm(3000,-2,0.5))
gmm=AdaptGauss::AdaptGauss(data,
Means = c(-2, 2, 7),
SDs = c(0.5, 1, 4),
Weights = c(0.3333, 0.3333, 0.3333))
AdaptGauss::Chi2testMixtures(data,
gmm$Means,gmm$SDs,gmm$Weights,PlotIt=T)
AdaptGauss::QQplotGMM(data,gmm$Means,gmm$SDs,gmm$Weights)
## End(Not run)
## Statistically non significant GMM
## Not run:
data('LKWFahrzeitSeehafen2010')
gmm=AdaptGauss::AdaptGauss(LKWFahrzeitSeehafen2010,
Means = c(52.74, 385.38, 619.46, 162.08),
SDs = c(38.22, 93.21, 57.72, 48.36),
Weights = c(0.2434, 0.5589, 0.1484, 0.0749))
AdaptGauss::Chi2testMixtures(LKWFahrzeitSeehafen2010,
gmm$Means,gmm$SDs,gmm$Weights,PlotIt=T)
AdaptGauss::QQplotGMM(LKWFahrzeitSeehafen2010,gmm$Means,gmm$SDs,gmm$Weights)
## End(Not run)
```

*AdaptGauss*version 1.6 Index]