ANFIS-class: ANFIS S4 class implementation in R

Description

Represent a concrete S4 class that represents an Adaptive Neuro Fuzzy Inference System in R, using type 3 Takagi and Sugeno's fuzzy if-then rule with multiple outputs.

Arguments

Slots

premises: list with the MembershipFunctions for each input.
consequents: numeric matrix with nrow= #rules, ncol= #outputs.
rules: matrix with the connectivity of the membership functions to the rules.
X: input matrix with ncol=#inputs and nrow=#individuals.
Y: output matrix with ncol=#output and nrow=#individuals.
errors: numeric vector with training errors.
trainingType: character describing the training algorithm used: trainHybridJangOffLine, trainHybridOffLine or trainHybridJangOnLine.
fitted.values: numeric matrix with predicted values for training data X.
residuals: numeric matrix with residuals values for training data X.
call: call class object with training call.

Features

Membership Functions (MF) flexible framework:
- Flexible user-defined membership functions(MF) extensible class.
- Independent number of (MF) for each input.
- Different MF types, if required, for each input.
Type 3 Takagi and Sugeno's fuzzy if-then rule
Full Rule combinations, e.g. 2 inputs 2 membership functions this means that 4 fuzzy rules will be created.
Different learning strategies:

trainHybridJangOffLine
Hybrid learning, i.e. Descent Gradient for precedents and Least Squares Estimation for consequents.

trainHybridJangOnLine
on-line version with hybrid learning.

trainHybridOffLine
Adaptive learning coefficient and momentum term.
Multiple outputs support, i.e., the same input partition can be used to predict more than one output variable.

Functions

ANFIS S4 class includes the following functions:

initialize: constructor of ANFIS Architecture to generate the rule set and consequents
show/print: generic output of the object
getRules, getPremises, getConsequents, getErrors, getTrainingType: return the respective ANFIS slots
plotMF: plot MembershipFunctions domain
plotMFs: plot all the MembershipFunctions for the input domain
plot: plot training error according with training Type
LSE: auxiliary function for Least Square Estimation to avoid singular matrix system in off-line training
trainHybridJangOffLine: Jang's Hybrid off-line training
trainHybridJangOnLine: Jang's Hybrid on-line training
trainHybridOffLine: Hybrid off-line training with momentum and adaptive learning rate
summary, fitted, fitted.values, coef, coefficients, resid, residuals: wrappers for traditional model functions

Other ANFIS: LSE, LSE, LSE,ANFIS-method, LSE-methods, trainHybridJangOffLine, trainHybridJangOffLine, trainHybridJangOffLine,ANFIS-method, trainHybridJangOffLine-methods, trainHybridJangOnLine, trainHybridJangOnLine, trainHybridJangOnLine,ANFIS-method, trainHybridJangOnLine-methods, trainHybridOffLine, trainHybridOffLine, trainHybridOffLine,ANFIS-method, trainHybridOffLine-methods; anfis3; coef, coef,ANFIS-method, coefficients, coefficients,ANFIS-method, fitted, fitted,ANFIS-method, fitted.values, fitted.values,ANFIS-method, resid, resid,ANFIS-method, residuals, residuals,ANFIS-method, summary, summary,ANFIS-method; getConsequents, getConsequents, getConsequents,ANFIS-method, getConsequents,ANFIS-method, getErrors, getErrors, getErrors,ANFIS-method, getErrors,ANFIS-method, getPremises, getPremises, getPremises,ANFIS-method, getPremises-methods, getRules, getRules, getRules,ANFIS-method, getRules-methods, getTrainingType, getTrainingType, getTrainingType,ANFIS-method, getTrainingType,ANFIS-method; initialize, initialize,ANFIS-method; plotMF, plotMF, plotMF,ANFIS-method, plotMF-methods, plotMFs, plotMFs, plotMFs,ANFIS-method, plotMFs-methods; plot, plot,ANFIS-method; predict, predict,ANFIS-method; print, print,ANFIS-method, show, show,ANFIS-method; trainSet

Examples

Run this code

##Set 2 cores using global options for parallel library
require("parallel")
if(.Platform$OS.type == "windows"){
 options(mc.cores=1)
}else{
 options(mc.cores=2) ##You could use all calling detectCores()
}

##Example domain for bidimentional sinc(x,y) function
x <- seq(-10, 10, length= 11)
trainingSet <- trainSet(x,x)
Z <- matrix(trainingSet[,"z"],ncol=length(x),nrow=length(x))
persp(x,x,Z,theta = 45, phi = 15, expand = 0.8, col = "lightblue",
 ticktype="detailed",main="sinc(x)*sinc(y)")

##Training domain patterns
X <- trainingSet[,1:2]
Y <- trainingSet[,3,drop=FALSE]

##Defining the required MembershipFunctions for the ANFIS
membershipFunction<-list(
 x=c(new(Class="NormalizedGaussianMF",parameters=c(mu=-10,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=-5,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=0,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=5,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=10,sigma=2))),
 y=c(new(Class="NormalizedGaussianMF",parameters=c(mu=-10,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=-5,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=0,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=5,sigma=2)),
   new(Class="NormalizedGaussianMF",parameters=c(mu=10,sigma=2))))

##Creating the ANFIS network with 2 inputs and 4 MembershipFunctions in
##each input
anfis3 <- new(Class="ANFIS",X,Y,membershipFunction)
anfis3

##Check for epsilon-completeness in each input
plotMFs(anfis3)

##Training the ANFIS network.
trainOutput <- trainHybridJangOffLine(anfis3, epochs=10)
##We will use instead an already trained object to reduce example time.
data(anfis3)

##How the training went. You can keep on training as the training error
##is still descending.
plot(anfis3)

##Test the fit, i. e., how the MembershipFunctions partition the input space
plotMFs(anfis3)

##Just to see if premises, consequents and errors were updated
getPremises(anfis3)[[input=1]][[mf=1]]
getConsequents(anfis3)[1:2,]
getErrors(anfis3) #Training errors
getTrainingType(anfis3)
names(coef(anfis3))
##An alternative to get premises and/or consequents ...
coef(anfis3)$premises[[input=1]][[mf=1]]
coef(anfis3)$consequents[1:2,]

##First five train pattern associated values for the training process
fitted(anfis3)[1:5,]
resid(anfis3)[1:5,]
summary(anfis3)

##Surface comparison between the original training set and the predicted
##ANFIS network
y <- predict(anfis3,X)
z <- matrix(y[,1],ncol=length(x),nrow=length(x))
par(mfrow=c(1,2))
persp(x,x,Z,theta = 45, phi = 15, expand = 0.8, col = "lightblue",
 ticktype="detailed",main="Goal")
persp(x,x,z,theta = 45, phi = 15, expand = 0.8, col = "lightblue",
 ticktype="detailed",main="Fitted training Patterns", zlim=c(min(Z),max(Z)))

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