Non-hierarchical evolutionary multi-objective optimization with local cutoff optimization

Description

NHEMO_Cutoff performs cost-sensitive classification by solving the non-hierarchical evolutionary two-objective optimization problem of minimizing misclassification rate and minimizing total costs for classification. NHEMO_Cutoff is based on an EMOA with tree representation and local cutoff optimization. Cutoffs of the tree learner are optimized analogous to a classification tree with recursive partitioning either based on the Gini index or the misclassification rate.

Usage

NHEMO_Cutoff(data, CostMatrix, 
             gens = 50, popsize = 50, max_nodes = 10, 
             ngens = 14, bound = 10^-10, 
             init_prob = 0.8, 
             ps = c("tournament", "roulette", "winkler"), tournament_size = 4, 
             crossover = c("standard", "brood", "poli"), brood_size = 4, 
             crossover_prob = 0.5, mutation_prob = 0.5, 
             CV = 5, vim = 0, 
             ncutoffs = 10, opt = c("gini", "mcr"))

Arguments

Details

The non-hierarchical evolutionary multi-objective tree learner (NHEMOtree) with local cutoff optimization solves a two-objective optimization problem with regard to minimizing misclassification rate and minimizing total costs for classification (summarized costs for all used variables in the classifier). It is based on an EMOA with tree representation. It optimizes both objectives simultaneously without any hierarchy and generates Pareto-optimal classifiers being binary trees to solve the problem. Cutoffs of the tree learner are optimized analogous to a classification tree with recursive partitioning either based on the Gini index or the misclassification rate.

Termination criteria of NHEMO_Cutoff are the maximal amount of generations and the Online Convergence Detection (OCD) proposed by Wagner and Trautmann (2010). Here, OCD uses the dominated hypervolume as quality criterion. If its variance over the last g generations is significantly below a given threshold L according to the one-sided χ^2-variance test OCD stops the run. We followed the suggestion of Wagner and Trautmann (2010) and considered their parameter settings as default values.

Missing data in the grouping variable or the explanatory variables are excluded from the analysis automatically. NHEMO_Cutoff does not work with missing data in "CostMatrix". Costs of all explanatory variables set to 1 results in optimizing the amount of explanatory variables in the tree learner as second objective.

Author(s)

Swaantje Casjens

References

R. Poli and W.B. Langdon. Schema theory for genetic programming with one-point crossover and point mutation. Evolutionary Computation, 6(3):231-252, 1998a.

W.A. Tackett. Recombination, selection und the genetic construction of computer programs. PhD thesis, University of Southern California, 1994.

T. Wagner and H. Trautmann. Online convergence detection for evolutionary multiobjective algorithms revisited. In: IEEE Congress on Evolutionary Computation, 1-8, 2010.

See Also

NHEMOtree

Examples

# Simulation of data and costs
  d         <- Sim_Data(Obs=200)
  CostMatrix<- Sim_Costs()

# NHEMO_Cutoff calculations with function NHEMOtree and type="NHEMO_Cutoff"
  res<- NHEMOtree(method="NHEMO_Cutoff", formula=Y2~., data=d, CostMatrix=CostMatrix, 
                  gens=5, popsize=5,
                  max_nodes=5, ngens=5, bound=10^-10, init_prob=0.8, 
                  ps="tournament", tournament_size=4, crossover="standard", 
                  crossover_prob=0.1, mutation_prob=0.1, 
                  CV=5, vim=1,
                  ncutoffs=5, opt="mcr")
  res

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)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(NHEMOtree)
Loading required package: partykit
Loading required package: grid
Loading required package: emoa
Loading required package: sets
Loading required package: rpart
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/NHEMOtree/NHEMO_Cutoff.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NHEMO_Cutoff
> ### Title: Non-hierarchical evolutionary multi-objective optimization with
> ###   local cutoff optimization
> ### Aliases: NHEMO_Cutoff
> ### Keywords: Non-hierarchical evolutionary multi-objective tree learner
> ###   Multi-objective optimization Evolutionary algorithms Classification
> 
> ### ** Examples
> 
> # Simulation of data and costs
>   d         <- Sim_Data(Obs=200)
>   CostMatrix<- Sim_Costs()
> 
> # NHEMO_Cutoff calculations with function NHEMOtree and type="NHEMO_Cutoff"
>   res<- NHEMOtree(method="NHEMO_Cutoff", formula=Y2~., data=d, CostMatrix=CostMatrix, 
+                   gens=5, popsize=5,
+                   max_nodes=5, ngens=5, bound=10^-10, init_prob=0.8, 
+                   ps="tournament", tournament_size=4, crossover="standard", 
+                   crossover_prob=0.1, mutation_prob=0.1, 
+                   CV=5, vim=1,
+                   ncutoffs=5, opt="mcr")
>   res
S metric:                     5857.598 
Misclassification (min/max):  23.25246 48.90833 
Costs (min/max):              17.85714 46.42857 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>