Below are the solutions to these exercises on neural network.
#################### # # # Exercise 1 # # # #################### set.seed(42) x<-runif(200, -10, 10) y<-sin(x) #################### # # # Exercise 2 # # # #################### weight<-runif(10, -1, 1) #################### # # # Exercise 3 # # # #################### set.seed(42) index<-sample(1:length(x),round(0.75*length(x)),replace=FALSE) reg.train<-data.frame(X=x[index],Y=y[index]) reg.test<-data.frame(X=x[-index],Y=y[-index]) #################### # # # Exercise 4 # # # #################### library(nnet) set.seed(42) reg.model.1<-nnet(reg.train$X,reg.train$Y,size=3,maxit=50,Wts=weight,linout=TRUE)
## # weights: 10 ## initial value 103.169943 ## iter 10 value 70.636986 ## iter 20 value 69.759785 ## iter 30 value 63.215384 ## iter 40 value 45.634297 ## iter 50 value 39.876476 ## final value 39.876476 ## stopped after 50 iterations
str(reg.model.1)
## List of 15 ## $ n : num [1:3] 1 3 1 ## $ nunits : int 6 ## $ nconn : num [1:7] 0 0 0 2 4 6 10 ## $ conn : num [1:10] 0 1 0 1 0 1 0 2 3 4 ## $ nsunits : num 5 ## $ decay : num 0 ## $ entropy : logi FALSE ## $ softmax : logi FALSE ## $ censored : logi FALSE ## $ value : num 39.9 ## $ wts : num [1:10] -7.503 2.202 3.004 -0.806 -4.69 ... ## $ convergence : int 1 ## $ fitted.values: num [1:150, 1] -0.196 0.568 -0.353 -0.205 -0.161 ... ## ..- attr(*, "dimnames")=List of 2 ## .. ..$ : NULL ## .. ..$ : NULL ## $ residuals : num [1:150, 1] 0.692 0.3079 -0.0398 0.4262 -0.7024 ... ## ..- attr(*, "dimnames")=List of 2 ## .. ..$ : NULL ## .. ..$ : NULL ## $ call : language nnet.default(x = reg.train$X, y = reg.train$Y, size = 3, Wts = weight, linout = TRUE, maxit = 50) ## - attr(*, "class")= chr "nnet"
#################### # # # Exercise 5 # # # #################### predict.model.1<-predict(reg.model.1,data.frame(X=reg.test$X)) str(predict.model.1)
## num [1:50, 1] -0.201 0.184 -0.873 -0.981 0.598 ... ## - attr(*, "dimnames")=List of 2 ## ..$ : NULL ## ..$ : NULL
rmse.reg<-sqrt(sum((reg.test$Y-predict.model.1)^2)) rmse.reg
## [1] 3.41651
plot(sin, -10, 10) points(reg.test$X,predict.model.1)
#################### # # # Exercise 6 # # # #################### set.seed(42) reg.model.2<-nnet(reg.train$X,reg.train$Y,size=7,maxit=50,Wts=runif(22, -1, 1),linout=TRUE)
## # weights: 22 ## initial value 353.642846 ## iter 10 value 55.906010 ## iter 20 value 42.700328 ## iter 30 value 22.757713 ## iter 40 value 16.910492 ## iter 50 value 12.770497 ## final value 12.770497 ## stopped after 50 iterations
str(reg.model.2)
## List of 15 ## $ n : num [1:3] 1 7 1 ## $ nunits : int 10 ## $ nconn : num [1:11] 0 0 0 2 4 6 8 10 12 14 ... ## $ conn : num [1:22] 0 1 0 1 0 1 0 1 0 1 ... ## $ nsunits : num 9 ## $ decay : num 0 ## $ entropy : logi FALSE ## $ softmax : logi FALSE ## $ censored : logi FALSE ## $ value : num 12.8 ## $ wts : num [1:22] 0.894 0.992 1.997 1.506 8.113 ... ## $ convergence : int 1 ## $ fitted.values: num [1:150, 1] 0.585 0.6145 -0.464 0.0943 -0.8862 ... ## ..- attr(*, "dimnames")=List of 2 ## .. ..$ : NULL ## .. ..$ : NULL ## $ residuals : num [1:150, 1] -0.0891 0.2612 0.071 0.1269 0.0232 ... ## ..- attr(*, "dimnames")=List of 2 ## .. ..$ : NULL ## .. ..$ : NULL ## $ call : language nnet.default(x = reg.train$X, y = reg.train$Y, size = 7, Wts = runif(22, -1, 1), linout = TRUE, maxit = 50) ## - attr(*, "class")= chr "nnet"
predict.model.2<-predict(reg.model.2,data.frame(X=reg.test$X)) str(predict.model.2)
## num [1:50, 1] 1.13 0.153 -0.931 -0.962 0.647 ... ## - attr(*, "dimnames")=List of 2 ## ..$ : NULL ## ..$ : NULL
rmse.reg<-sqrt(sum((reg.test$Y-predict.model.2)^2)) rmse.reg
## [1] 2.188407
plot(sin, -10, 10) points(reg.test$X,predict.model.2)
#################### # # # Exercise 7 # # # #################### data<-iris scale.data<-data.frame(lapply(data[,1:4], function(x) scale(x))) scale.data$Species<-data$Species index<-sample(1:nrow(scale.data),round(0.75*nrow(scale.data)),replace=FALSE) clust.train<-scale.data[index,] clust.test<-scale.data[-index,] #################### # # # Exercise 8 # # # #################### set.seed(42) clust.model<-nnet(Species~.,size=10,Wts=runif(83, -1, 1),data=clust.train)
## # weights: 83 ## initial value 187.294915 ## iter 10 value 10.386561 ## iter 20 value 5.337510 ## iter 30 value 2.311922 ## iter 40 value 1.426508 ## iter 50 value 1.387440 ## iter 60 value 1.386324 ## final value 1.386294 ## converged
#################### # # # Exercise 9 # # # #################### predict.model.clust<-predict(clust.model,clust.test[,1:4],type="class") #################### # # # Exercise 10 # # # #################### Table<-table(clust.test$Species ,predict.model.clust) Table
## predict.model.clust ## setosa versicolor virginica ## setosa 16 0 0 ## versicolor 0 9 0 ## virginica 0 0 13
accuracy<-sum(diag(Table))/sum(Table) accuracy
## [1] 1
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very nice presentation of ANN in R; pattern recog; and regress; function approx; pl. upload some on optimization also using ANN; GA etc