AdaptGauss (version 1.2.0)

AdaptGauss: Adapt Gaussian Mixture Model (GMM)

Description

Adapt interactively a Gaussians Mixture Model GMM to the empirical PDF of the data (generated by ParetoDensityEstimation) such that N(Means,SDs)*Weights is a model for Data

Usage

AdaptGauss(Data,Means,SDs,Weights,ParetoRadius,LB,HB,ListOfAdaptGauss,fast)

Arguments

Data

Data for empirical PDF. Has to be an Array of values. NaNs and NULLs will be deleted

Means

Optional: Means of gaussians of GMM.

SDs

Optional: StandardDevations of gaussians of GMM. (Has to be the same length as Means)

Weights

Optional: Weights of gaussians of GMM. (Has to be the same length as Means)

ParetoRadius

Optional: Pareto Radius of Pareto Desity Estimation (PDE).

LB

Optional: Low boundary of estimation. All values below LB will be deleted. Default: min(Data)

HB

Optional: High boundary of estimation. All values above HB will be deleted. Default: max(Data)

ListOfAdaptGauss

Optional: If editing of an existing Model is the goal, enables to give the Output of AdaptGaus as the Input of AdaptGauss() instead of setting Means, SDs and Weights separately

fast

Default=TRUE; FALSE: Using mclust's EM see function densityMclust of that package, TRUE: Naive but faster EM implementation, which may be numerical unstable, because log(gauss) is not used

Value

• List with
• Means
  Means of Gaussian's.
• SDs
  Standard SDs of Gaussian's.
• Weights
  Weights of Gaussian's.
• ParetoRadius
  Pareto Radius: Either ParetoRadiusIn, the pareto radius enerated by PretoDensityEstimation(if no Pareto Radius in Input).
• RMS
  Root Mean Square of Deviation between Gaussian Mixture Model GMM to the empirical PDF. Normalized by RMS of one Gaussian with mean=meanrobust(data) and sdev=stdrobust(data). Further Details in [Ultsch et al 2015]
• BayesBoundaries
  vector[1:L-1], Bayes decision boundaries

Details

Data: maximum length is 10000. If larger, Data will be randomly reduced to 10000 Elements. MeansIn/DeviationsIn/WeightsIN: If empty, either one or three Gaussian's are generated by kmeans algorithm. Pareto Radius: If empty: will be generated by ParetoDensityEstimation RMS: Root Mean Square error is normalized by RMS of Gaussian's with Mean=mean(data) and SD=sd(data), see [Ultsch et.al., 2015] for further details.

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. 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

data1=c(rnorm(1000))
  Vals1=AdaptGauss(data1)
  
  data2=c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
  Vals2=AdaptGauss(data2,c(-1,0,2),c(2,1,1),c(0.25,0.25,0.5),0.3,-6,6)