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Last data update: 2014.03.03

R: Pareto Density Estimation

ParetoDensityEstimation

R Documentation

Pareto Density Estimation

Description

This function estimates the Pareto Density for the distribution of one variable.

Usage

ParetoDensityEstimation(Data,paretoRadius,kernels,MinAnzKernels)

Arguments

`Data`	numeric vector of data.
`paretoRadius`	Optional, numeric value, see `ParetoRadius`
`kernels`	Optional, numeric vector. data values where pareto density is measured at. If 0 (by default) kernels will be computed.
`MinAnzKernels`	Optional, minimal number of kernels, default MinAnzKernels==100

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters.

Value

List with

`kernels`	numeric vector. data values at with Pareto Density is measured.
`paretoDensity`	numeric vector containing the determined density by ParetoRadius.
`paretoRadius`	numeric value.

Note

This is the best density estimation to judge Gaussian Mixtures of the data see [Ultsch 2003]

Author(s)

Michael Thrun

References

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.

Examples

			data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
			# Optional, if not given ParetoDensityEstimation() 
			# calls ParetoRadius()
			pareto_radius<-ParetoRadius(data) 
			pdeVal        <- ParetoDensityEstimation(data,pareto_radius)
			plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
			yaxs='i',xlab='Data',ylab='PDE')

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(AdaptGauss)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/AdaptGauss/ParetoDensityEstimation.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ParetoDensityEstimation
> ### Title: Pareto Density Estimation
> ### Aliases: ParetoDensityEstimation
> 
> ### ** Examples
> 
> 			data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
> 			# Optional, if not given ParetoDensityEstimation() 
> 			# calls ParetoRadius()
> 			pareto_radius<-ParetoRadius(data) 
> 			pdeVal        <- ParetoDensityEstimation(data,pareto_radius)
> 			plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
+ 			yaxs='i',xlab='Data',ylab='PDE') 
>   			
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>