##plot the first few examples:
if(i<=4)
{
image(matrix(s,10,10,byrow=T),main="S example",col=grey(100:0/100))
image(matrix(x,10,10,byrow=T),main  = "X example",col=grey(100:0/100))
}
dataX[i,] <- x
dataS[i,] <- s
}
data <- rbind(dataX,dataS)
merged <- data.frame(letter=as.factor(letter),data)
model3  <- nnet(letter~.,data=merged,size=2,rarg=.1,decay=.0001,maxit=500)
table(letter,predict(model3,type="class"))
library(MASS)
library(DAAG)
feature1 <- rnorm(200)
feature2 <- rnorm(200)
outcome <- as.factor((feature1 > .6 & feature2 > .3) | (feature1>.6 & feature2<.3))
outcome <- as.factor((feature1 * (-feature2) + rnorm(200))>0)
lmodel <-  lda(outcome~feature1+feature2)
confusion(outcome,predict(lmodel)$class)
lmodel2 <-  lda(outcome~feature1*feature2)
confusion(outcome,predict(lmodel2)$class)
n1 <- nnet(outcome~feature1+feature2,size=0,skip=TRUE)
confusion(outcome,factor(predict(n1,type="class"),levels=c(TRUE,FALSE)))
n2 <- nnet(outcome~feature1+feature2,size=3,skip=TRUE)
confusion(outcome,factor(predict(n2,type="class"),levels=c(FALSE,TRUE)))
phone <- read.csv("data_study1.csv")
phone$Smartphone <- (as.factor(phone$Smartphone))
phone$Gender <- as.numeric(as.factor(phone$Gender))
set.seed(100)
phonemodel <- nnet(Smartphone~.,size=3,data=phone)
confusion(phone$Smartphone,factor(predict(phonemodel,newdata=phone,type="class",levels=c("Android","iPhone"))))
set.seed(101)
phonemodel2 <- nnet(Smartphone~.,data=phone,size=2)
confusion(phone$Smartphone,factor(predict(phonemodel2,newdata=phone,type="class"),levels=c("Android","iPhone")))
preds <- matrix(0,100)
for(i in 1:100)
{
phonemodel3 <- nnet(Smartphone~.,data=phone,size=2)
preds[i] <- confusion(phone$Smartphone,factor(predict(phonemodel3,newdata=phone,type="class"),levels=c("Android","iPhone")))$overall
}
hist(preds,col="gold",main="Accuracy of 100 fitted models (2 hidden nodes)",xlim=c(0,1))
preds <- matrix(0,100)
for(i in 1:100)
{
phonemodel3 <- nnet(Smartphone~.,data=phone,size=6)
preds[i] <- confusion(phone$Smartphone,factor(predict(phonemodel3,newdata=phone,type="class"),levels=c("Android","iPhone")))$overall
}
hist(preds,col="gold",main="Accuracy of 100 fitted models (6 hidden nodes)",xlim=c(0,1))
train <- rep(FALSE,nrow(phone))
train[sample(1:nrow(phone),size=300)] <- TRUE
test <- !train
phonemodel2 <- nnet(Smartphone~.,data=phone,size=6,subset=train)
confusion(phone$Smartphone[test],
predict(phonemodel2,newdata=phone[test,],type="class"))
preds <- rep(0,100)
for(i in 1:100)
{
train <- rep(FALSE,nrow(phone))
train[sample(1:nrow(phone),size=300)] <- TRUE
test <- !train
phonemodel2 <- nnet(Smartphone~.,data=phone,size=6,subset=train)
preds[i] <-  confusion(phone$Smartphone[test],factor(predict(phonemodel2,newdata=phone[test,],type="class"),levels=c("Android","iPhone")))$overall
}
hist(preds,col="gold",main="Accuracy of 100 cross-validated models (6 hidden nodes)",xlim=c(0,1))
preds <- rep(0,100)
for(i in 1:100)
{
train <- rep(FALSE,nrow(phone))
train[sample(1:nrow(phone),size=300)] <- TRUE
test <- !train
phonemodel2 <- nnet(Smartphone~Gender+Avoidance.Similarity+Phone.as.status.object+Age,
data=phone,size=6,subset=train)
preds[i] <-  confusion(phone$Smartphone[test],factor(predict(phonemodel2,newdata=phone[test,],type="class"),levels=c("Android","iPhone")))$overall
}
hist(preds,col="gold",main="Accuracy of 100 cross-validated models (6 hidden nodes)",xlim=c(0,1))
library(neuralnet)
set.seed(10313)
train <- rep(FALSE,nrow(phone))
train[sample(1:nrow(phone),size=300)] <- TRUE
test <- !train
phonemodel3 <- neuralnet(Smartphone~.,
hidden=c(2,2),
data=phone[train,])
pred <- apply(predict(phonemodel3,newdata=phone[test,]),1,which.max)
ptest <- phone[test,]
acc <- (sum(ptest[pred==1,]$Smartphone=="Android") + sum(ptest[pred==2,]$Smartphone=="iPhone") )/sum(test)
print(acc)
plot(phonemodel3,rep="best")
library(neuralnet)
library(DAAG)
##10K examples of 0 to 9
mnistdat <-read.csv("mnist_test.csv")
mnistdat$label <- factor(mnistdat$label) ## this needs to be a factor if it has more than 2 levels
mnist47 <- mnistdat[mnistdat$label==4 | mnistdat$label==7| mnistdat$label==9,]
train <- mnist47[sample(1:nrow(mnist47),1000),]  #train on some examples
set.seed(100)
mnist <- neuralnet(label~.,
hidden=c(4),
data=train)
##examine the trained data:
table(train$label,c(4,7,9)[apply(mnist$response,1,which.max)])
p2 <- predict(mnist,newdata=mnist47)
pred <- c(4,7,9)[apply(p2,1,which.max)]
table(mnist47$label,pred)
mean(mnist47$label==pred)
set.seed(101)
mnist33 <- neuralnet(label~.,
hidden=c(4,3), algorithm="backprop",rep=5,learningrate=.001,stepmax=5000,
lifesign="full",lifesign.step=1000,
data=train)
##examine the trained data:
table(train$label,c(4,7,9)[apply(mnist33$response,1,which.max)])
p2 <- predict(mnist33,newdata=mnist47)
error47 <- mnist47[mnist47$label==4 & pred==7,]
cols <- grey(100:1/100)
par(mfrow=c(2,4))
image((matrix(as.numeric(error47[1,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[2,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[3,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[4,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[5,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[6,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[7,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[8,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
library(neuralnet)
library(DAAG)
##10K examples of 0 to 9
mnistdat <-read.csv("mnist_test.csv")
mnistdat$label <- factor(mnistdat$label) ## this needs to be a factor if it has more than 2 levels
mnist47 <- mnistdat[mnistdat$label==4 | mnistdat$label==7| mnistdat$label==9,]
train <- mnist47[sample(1:nrow(mnist47),1000),]  #train on some examples
set.seed(100)
mnist <- neuralnet(label~.,
hidden=c(4),
data=train)
##examine the trained data:
table(train$label,c(4,7,9)[apply(mnist$response,1,which.max)])
p2 <- predict(mnist,newdata=mnist47)
pred <- c(4,7,9)[apply(p2,1,which.max)]
table(mnist47$label,pred)
mean(mnist47$label==pred)
library(neuralnet)
library(DAAG)
##10K examples of 0 to 9
mnistdat <-read.csv("mnist_test.csv")
mnistdat$label <- factor(mnistdat$label) ## this needs to be a factor if it has more than 2 levels
mnist47 <- mnistdat[mnistdat$label==4 | mnistdat$label==7| mnistdat$label==9,]
train <- mnist47[sample(1:nrow(mnist47),1000),]  #train on some examples
set.seed(100)
mnist <- neuralnet(label~.,
hidden=c(4),
data=train)
##examine the trained data:
table(train$label,c(4,7,9)[apply(mnist$response,1,which.max)])
p2 <- predict(mnist,newdata=mnist47)
pred <- c(4,7,9)[apply(p2,1,which.max)]
table(mnist47$label,pred)
mean(mnist47$label==pred)
error47 <- mnist47[mnist47$label==4 & pred==7,]
cols <- grey(100:1/100)
par(mfrow=c(2,4))
image((matrix(as.numeric(error47[1,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[2,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[3,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[4,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[5,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[6,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[7,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error47[8,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
error49 <- mnist47[mnist47$label==4 & pred==9,]
cols <- grey(100:1/100)
par(mfrow=c(2,4))
image((matrix(as.numeric(error49[1,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[2,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[3,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[4,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[5,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[6,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[7,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
image((matrix(as.numeric(error49[8,-1]),nrow=28,ncol=28))[,28:1],xaxt="n",yaxt="n",col=cols,main="4s called 7s")
means <- tapply(as.numeric(dat$Age),list(dat$Smartphone),mean)
library(knitr)
library(rmdformats)
## Global options
options(max.print="75")
opts_chunk$set(echo=TRUE,
cache=TRUE,
prompt=FALSE,
tidy=TRUE,
comment=NA,
message=FALSE,
warning=FALSE)
opts_knit$set(width=75)
dat <- read.csv("data_study1.csv")
dat$Smartphone <- factor(dat$Smartphone)
library(klaR)
nb <- NaiveBayes(Smartphone~.,data=dat)
library(DAAG)
summary(nb)
nb$apriori
nb$tables
means <- tapply(as.numeric(dat$Age),list(dat$Smartphone),mean)
sds <- tapply(as.numeric(dat$Age),list(dat$Smartphone),sd)
means
sds
library(ggplot2)
phone <- rep(c("iphone","android"),each=100)
density<-c(dnorm(1:100,mean=means[2],sd=sds[2]),
dnorm(1:100,mean=means[1],sd=sds[1]))
df <- data.frame(age=c(1:100,1:100),
phone,density)
ggplot(df,aes(x=age,y=density,colour=phone)) + geom_line()
library(ggplot2)
phone <- rep(c("iphone","android"),each=100)
density<-c(dnorm(1:100,mean=means[2],sd=sds[2]),
dnorm(1:100,mean=means[1],sd=sds[1]))
df <- data.frame(age=c(1:100,1:100),
phone,density)
ggplot(df,aes(x=age,y=density,colour=phone)) + geom_line() + theme_bw() + scale_color_manual(values=c("orange4","navy"))
library(ggplot2)
phone <- rep(c("iphone","android"),each=100)
density<-c(dnorm(1:100,mean=means[2],sd=sds[2]),
dnorm(1:100,mean=means[1],sd=sds[1]))
df <- data.frame(age=c(1:100,1:100),
phone,density)
ggplot(df,aes(x=age,y=density,colour=phone)) + geom_line() + theme_bw() + scale_color_manual(values=c("orange2","navy"))
library(ggplot2)
phone <- rep(c("iphone","android"),each=100)
density<-c(dnorm(1:100,mean=means[2],sd=sds[2]),
dnorm(1:100,mean=means[1],sd=sds[1]))
df <- data.frame(age=c(1:100,1:100),
phone,density)
ggplot(df,aes(x=age,y=density,colour=phone)) + geom_line(size=2) + theme_bw() + scale_color_manual(values=c("orange2","navy"))
df <- data.frame(age=c(1:100),
lr =
(dnorm(1:100,mean=means[2],sd=sds[2])/
dnorm(1:100,mean=means[1],sd=sds[1]))
)
ggplot(df,aes(x=age,y=lr)) + geom_line() + geom_hline(yintercept=1)+ theme_bw() + scale_color_manual(values=c("orange2","navy"))
pred <- predict(nb)
confusion(dat$Smartphone,pred$class)
nb2 <- NaiveBayes(Smartphone~.,usekernel=T,data=dat)
nb2$tables
plot(nb2)
pred2 <- predict(nb2)
confusion(dat$Smartphone,pred2$class)
?NaiveBayes
nb2 <- NaiveBayes(Smartphone~.,usekernel=T,data=dat)
nb2$tables
plot(nb2, col=c("navy","orange2"))
nb2 <- NaiveBayes(Smartphone~.,usekernel=T,data=dat)
nb2$tables
plot(nb2, col=c("navy","orange2"), lwd=1.5)
pred2 <- predict(nb2)
confusion(dat$Smartphone,pred2$class)
pred2 <- predict(nb2)
confusion(dat$Smartphone,pred2$class)
library(e1071)
data(dengue)
summary(dengue)
dengue$NoYes <- as.factor(dengue$NoYes)
library(e1071)
data(dengue)
summary(dengue)
dengue$NoYes <- as.factor(dengue$NoYes)
#This doesn't work
#nb.dengue <- NaiveBayes(NoYes~.,data=dengue)
nb.dengue <- NaiveBayes(NoYes~.,data=dengue,na.action="na.omit") ##this works
#This one works with the klaR NaiveBayes:
nb.dengue2 <- NaiveBayes(NoYes~ h10pix+Xmin+Ymin,data=dengue)
#this one works--from e1071 package
nb.dengue3<- naiveBayes(NoYes~.,data=dengue)
#when we remove the na, we need to remove it from the ground truth too:
confusion(dengue$NoYes[!is.na(rowMeans(dengue[,-9]))],predict(nb.dengue)$class)
confusion(dengue$NoYes,predict(nb.dengue2)$class)
confusion(dengue$NoYes,predict(nb.dengue3,newdata=dengue))
#This doesn't work
#nb.dengue <- NaiveBayes(NoYes~.,data=dengue)
nb.dengue <- NaiveBayes(NoYes~.,data=dengue,na.action="na.omit") ##this works
#This one works with the klaR NaiveBayes:
nb.dengue2 <- NaiveBayes(NoYes~ h10pix+Xmin+Ymin,data=dengue)
#this one works--from e1071 package
nb.dengue3<- naiveBayes(NoYes~.,data=dengue)
#when we remove the na, we need to remove it from the ground truth too:
confusion(dengue$NoYes[!is.na(rowMeans(dengue[,-9]))],predict(nb.dengue)$class)
confusion(dengue$NoYes,predict(nb.dengue2)$class)
confusion(dengue$NoYes,predict(nb.dengue3,newdata=dengue))
library(klaR)
library(DAAG)
train <-read.csv("trainmnist.csv")
test <- read.csv("testmnist.csv")
##smooth out the training set a bit by adding some noise, so no pixel
##has a sd of 0.
for(i in 1:ncol(train))
{
train[,i] <- rnorm(500,as.numeric(train[,i]),.1)
}
par(mfrow=c(2,4))
image(matrix(unlist(train[1,]),nrow=28))
image(matrix(unlist(train[2,]),nrow=28))
image(matrix(unlist(train[3,]),nrow=28))
image(matrix(colMeans(train[1:250,]),nrow=28))
image(matrix(unlist(train[251,]),nrow=28))
image(matrix(unlist(train[252,]),nrow=28))
image(matrix(unlist(train[253,]),nrow=28))
image(matrix(colMeans(train[251:500,]),nrow=28))
train$labels <- as.factor(rep(0:1,each=250))
nb3 <- NaiveBayes(labels~.,usekernel=T,data=train)
p3a <- predict(nb3) ##this takes a while
confusion(train$labels,p3a$class) ##almost perfect
p3b<- predict(nb3,test) ##equally good
confusion(rep(0:1,each=250),p3b$class)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),.35)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28))
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28))
p3c<- predict(nb3,test) ##This one is pretty bad.
confusion(rep(0:1,each=250),p3c$class)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),5)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28))
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28))
p3c<- predict(nb3,test) ##This one is pretty bad.
confusion(rep(0:1,each=250),p3c$class)
image(matrix(unlist(noisetest[251,]),nrow=28))
noisetest <- test
for(i in 1:ncol(test))
{
noisetest[,i] <- rnorm(500,as.numeric(test[,i]),3)
}
par(mfrow=c(2,4))
image(matrix(unlist(noisetest[1,]),nrow=28))
image(matrix(unlist(noisetest[2,]),nrow=28))
image(matrix(unlist(noisetest[3,]),nrow=28))
image(matrix(colMeans(noisetest[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(noisetest[251,]),nrow=28))
image(matrix(unlist(noisetest[252,]),nrow=28))
image(matrix(unlist(noisetest[253,]),nrow=28))
image(matrix(colMeans(noisetest[251:500,]),nrow=28),main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is pretty bad.
confusion(rep(0:1,each=250),p3c$class)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),1)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28), main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is still pretty good
confusion(rep(0:1,each=250),p3c$class)
set.seed(100)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),3)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28), main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is still pretty good
confusion(rep(0:1,each=250),p3c$class)
library(klaR)
library(DAAG)
train <-read.csv("trainmnist.csv")
test <- read.csv("testmnist.csv")
set.seed(101)
##smooth out the training set a bit by adding some noise, so no pixel
##has a sd of 0.
for(i in 1:ncol(train))
{
train[,i] <- rnorm(500,as.numeric(train[,i]),.1)
}
par(mfrow=c(2,4))
image(matrix(unlist(train[1,]),nrow=28))
image(matrix(unlist(train[2,]),nrow=28))
image(matrix(unlist(train[3,]),nrow=28))
image(matrix(colMeans(train[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(train[251,]),nrow=28))
image(matrix(unlist(train[252,]),nrow=28))
image(matrix(unlist(train[253,]),nrow=28))
image(matrix(colMeans(train[251:500,]),nrow=28), main="Average of 250 prototypes")
set.seed(100)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),1)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28), main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is still pretty good
confusion(rep(0:1,each=250),p3c$class)
library(klaR)
library(DAAG)
train <-read.csv("trainmnist.csv")
test <- read.csv("testmnist.csv")
set.seed(101)
##smooth out the training set a bit by adding some noise, so no pixel
##has a sd of 0.
for(i in 1:ncol(train))
{
train[,i] <- rnorm(500,as.numeric(train[,i]),.1)
}
par(mfrow=c(2,4))
image(matrix(unlist(train[1,]),nrow=28))
image(matrix(unlist(train[2,]),nrow=28))
image(matrix(unlist(train[3,]),nrow=28))
image(matrix(colMeans(train[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(train[251,]),nrow=28))
image(matrix(unlist(train[252,]),nrow=28))
image(matrix(unlist(train[253,]),nrow=28))
image(matrix(colMeans(train[251:500,]),nrow=28), main="Average of 250 prototypes")
train$labels <- as.factor(rep(0:1,each=250))
nb3 <- NaiveBayes(labels~.,usekernel=T,data=train)
p3a <- predict(nb3) ##this takes a while
confusion(train$labels,p3a$class) ##almost perfect
p3b<- predict(nb3,test) ##equally good
confusion(rep(0:1,each=250),p3b$class)
set.seed(100)
for(i in 1:ncol(test))
{
test[,i] <- rnorm(500,as.numeric(test[,i]),.25)
}
par(mfrow=c(2,4))
image(matrix(unlist(test[1,]),nrow=28))
image(matrix(unlist(test[2,]),nrow=28))
image(matrix(unlist(test[3,]),nrow=28))
image(matrix(colMeans(test[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(test[251,]),nrow=28))
image(matrix(unlist(test[252,]),nrow=28))
image(matrix(unlist(test[253,]),nrow=28))
image(matrix(colMeans(test[251:500,]),nrow=28), main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is still pretty good
confusion(rep(0:1,each=250),p3c$class)
noisetest <- test
for(i in 1:ncol(test))
{
noisetest[,i] <- rnorm(500,as.numeric(test[,i]),2)
}
par(mfrow=c(2,4))
image(matrix(unlist(noisetest[1,]),nrow=28))
image(matrix(unlist(noisetest[2,]),nrow=28))
image(matrix(unlist(noisetest[3,]),nrow=28))
image(matrix(colMeans(noisetest[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(noisetest[251,]),nrow=28))
image(matrix(unlist(noisetest[252,]),nrow=28))
image(matrix(unlist(noisetest[253,]),nrow=28))
image(matrix(colMeans(noisetest[251:500,]),nrow=28),main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is pretty bad.
confusion(rep(0:1,each=250),p3c$class)
train[1:5,]
noisetest <- test
for(i in 1:ncol(test))
{
train[i,1:784] <- rnorm(500,as.numeric(train[i,1:784]),2)
noisetest[,i] <- rnorm(500,as.numeric(test[,i]),2)
}
noisetest <- test
set.seed(100)
for(i in 1:ncol(test))
{
train[,i] <-     rnorm(500,as.numeric(train[,i]),2)
noisetest[,i] <- rnorm(500,as.numeric(test[,i]),2)
}
nb3 <- NaiveBayes(labels~.,usekernel=T,data=train)
par(mfrow=c(2,4))
image(matrix(unlist(noisetest[1,]),nrow=28))
image(matrix(unlist(noisetest[2,]),nrow=28))
image(matrix(unlist(noisetest[3,]),nrow=28))
image(matrix(colMeans(noisetest[1:250,]),nrow=28), main="Average of 250 prototypes")
image(matrix(unlist(noisetest[251,]),nrow=28))
image(matrix(unlist(noisetest[252,]),nrow=28))
image(matrix(unlist(noisetest[253,]),nrow=28))
image(matrix(colMeans(noisetest[251:500,]),nrow=28),main="Average of 250 prototypes")
p3c<- predict(nb3,test) ##This one is pretty bad.
confusion(rep(0:1,each=250),p3c$class)