AdaptGauss-package: AdaptGauss-package
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 [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.References
Alfred Ultsch, Michael C. Thrun, Onno Hansen-Goos, Joern Loetsch Identification of molecular fingerprints in heat pain thresholds by use of an interactive mixture model toolbox (AdaptGauss), IJMS 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 discover, 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.