DistributionOptimization {DistributionOptimization}

Distribution Fitting

Description

Fits a Gaussian Mixture Model onto a Dataset by minimizing a fitting error through evolutionary optimization. Every individual encodes one GMM. Details over the evolutionary process itself can be taken from the 'GA' package. ga

Usage

DistributionOptimization(Data, Modes, Monitor = 1,
  SelectionMethod = "UnbiasedTournament",
  MutationMethod = "Uniform+Focused",
  CrossoverMethod = "WholeArithmetic", PopulationSize = Modes * 3 * 25,
  MutationRate = 0.7, Elitism = 0.05, CrossoverRate = 0.2,
  Iter = Modes * 3 * 200, OverlapTolerance = NULL,
  IsLogDistribution = rep(F, Modes), ErrorMethod = "chisquare",
  NoBins = NULL, Seed = NULL, ConcurrentInit = F, ParetoRad = NULL)

Arguments

Data

Data to be modelled

Modes

Number of expected Modes

Monitor

0:no monitoring, 1: status messages, 2: status messages and plots, 3: status messages, plots and calculated error-measures

SelectionMethod

1: LinearRank selection 4: UnbiasedTournament 5: FitnessProportional selection

MutationMethod

1: UniformRandom mutation 2: NonuniformRandom mutation 4: Focused mutation, alternative random mutation around solution 5: GaussMutationCust 6: TwoPhaseMutation - mutation is uniform random during the first half of iterations, and than focuses around current solution

CrossoverMethod

1: single point crossover 2: whole arithmetic crossover 3: local arithmetic crossover 4: blend crossover 5: GaussCrossover - exchange complete gaussian components 6: MultiPointCrossover - Random amount of information between mixtures get exchanged

PopulationSize

Size of the population

MutationRate

amount (0..1) of population that gets mutated

Elitism

amount of best individuals that will survive generation unchanged

CrossoverRate

amount of individuals that will be used for crossover

Iter

number of iterations of this algorithm

OverlapTolerance

ratio between Chi-Square and OverlapError (only if FitnessMethod = 4 (Chi2ValueWithOverlap))

IsLogDistribution

which gauss components should be considered as log gaussian

ErrorMethod

"pde": fitting is measured by pareto density estimation. "chisquare": fitting is measured by Chi-Square test

NoBins

Number of Bins that will be used for evaluating fitting

Seed

Random Seed for reproducible results

ConcurrentInit

If true, before initialization a number of short optimizations are done to find a good starting point for evolution

ParetoRad

Pareto Radius for Pareto Density Estimation and its plots

Value

The GA object containing the evolutionary training and a description of the final GMM consisting of means, sdevs and weights.

Author(s)

Florian Lerch

Jorn Lotsch

Alfred Ultsch

Examples

## Not run: 
DistributionOptimization(c(rnorm(200),rnorm(200,3), 2))

## End(Not run)