f <- function(x,y,m1,m2){
exp(-0.5*c(x-m1,y-m2)%*%matrix(c(1,-0.5,-0.5,0.5),2)%*%c(x-m1,y-m2))/
sqrt((2*pi)^2*det(matrix(c(2,2,2,4),2)))
}

a <- rep(-15:40/5,56)
b <- rep(-15:40/5,rep(56,56))
fe<-c()
for(i in 1:(56*56)){
fe[i]<-f(a[i],b[i],1,2)
}
contour(-15:40/5,-15:40/5,matrix(fe,56),labex=c(),col='red')
for(i in 1:(56*56)){
fe[i]<-f(a[i],b[i],5,4)
}
contour(-15:40/5,-15:40/5,matrix(fe,56),add=T,labex=c(),col='blue')
abline(h=0,lty='dashed')
abline(v=0,lty='dashed')

for(i in 1:100) points(rnorm(2)%*%matrix(c(1,0,1,2),2)+c(1,2),col="red")
for(i in 1:100) points(rnorm(2)%*%matrix(c(1,0,1,2),2)+c(5,4),col="blue")

simuldata4 <- function(m){
x <- c(rnorm(m)/2, rnorm(m))
y <- c(rnorm(m)/2+1, rnorm(m)-0.5)
typ <- c(rep("blue",m),rep("red",m))
return(data.frame(x,y,typ))
}

lerndaten <- simuldata4(500)
plot(lerndaten$x,lerndaten$y,col=as.vector(lerndaten$typ),xlab="",ylab="")

daten <- data.frame(x=c(runif(100,-4,0),runif(100,0.5,2.5)),y=c(runif(100,-3,1),runif(100,0,3)),b=c(rep(-1,100),rep(1,100)))
plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
w <- c(0,0)
t <- 0
eta <- 1
R <- max(sqrt(daten$x^2+daten$y^2))
R
s <- split(1:200,(w[1]*daten$x+w[2]*daten$y+t)*daten$b>0)$"FALSE"
i<-0
while(length(s)>0) {
   if(length(s)>1) nr <- sample(s,1) else nr <- s
   plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
   points(daten$x[s],daten$y[s],pch=20+daten$b,col="red")
   lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5))
   arrows(0,0,w[1],w[2])
   points(daten$x[nr],daten$y[nr],col="blue",pch=20+daten$b[nr])
   arrows(0,0,daten$x[nr],daten$y[nr],col="blue")
   w <- w + eta * daten$b[nr] * c(daten$x[nr],daten$y[nr])
   t <- t + eta * daten$b[nr] * R^2
   lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5),col="green")
   arrows(0,0,w[1],w[2],col="green")
   s <- split(1:200,(w[1]*daten$x+w[2]*daten$y+t)*daten$b>0)$"FALSE"
   i<-i+1
   print(c("i=",i))
}
plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5))

library(MASS)
L <- lda(b~x+y,daten)
a <- rep(-40:40/10,81)
b <- rep(-40:40/10,rep(81,81))
P <- predict(L,data.frame("x"=a,"y"=b),type="probs")
contour(-40:40/10,-40:40/10,matrix(P[[2]][,1]-P[[2]][,2],81),
add=T,levels=0,labex=c(),col='red')

LM <- lm(b~x+y,daten)
lines(c(-4,+4),c((LM$coefficients[["(Intercept)"]]+4*LM$coefficients[["x"]])/LM$coefficients[["y"]],(LM$coefficients[["(Intercept)"]]-4*LM$coefficients[["x"]])/LM$coefficients[["y"]]),col="blue")


daten <- data.frame(x=c(runif(150,-4,0),runif(50,0.5,2.5)),y=c(runif(150,-3,1),runif(50,0,3)),b=c(rep(-1,150),rep(1,50)))
plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
w <- c(0,0)
t <- 0
eta <- 1
R <- max(sqrt(daten$x^2+daten$y^2))
R
s <- split(1:200,(w[1]*daten$x+w[2]*daten$y+t)*daten$b>0)$"FALSE"
i<-0
while(length(s)>0) {
   if(length(s)>1) nr <- sample(s,1) else nr <- s
   plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
   points(daten$x[s],daten$y[s],pch=20+daten$b,col="red")
   lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5))
   arrows(0,0,w[1],w[2])
   points(daten$x[nr],daten$y[nr],col="blue",pch=20+daten$b[nr])
   arrows(0,0,daten$x[nr],daten$y[nr],col="blue")
   w <- w + eta * daten$b[nr] * c(daten$x[nr],daten$y[nr])
   t <- t + eta * daten$b[nr] * R^2
   lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5),col="green")
   arrows(0,0,w[1],w[2],col="green")
   s <- split(1:200,(w[1]*daten$x+w[2]*daten$y+t)*daten$b>0)$"FALSE"
   i<-i+1
   print(c("i=",i))
}
plot(daten$x,daten$y,pch=20+daten$b,xlim=c(-5,5),ylim=c(-5,5))
lines(c(-(-5*w[2]+t)/w[1],-(5*w[2]+t)/w[1]),c(-5,5))

library(MASS)
L <- lda(b~x+y,daten)
a <- rep(-40:40/10,81)
b <- rep(-40:40/10,rep(81,81))
P <- predict(L,data.frame("x"=a,"y"=b),type="probs")
contour(-40:40/10,-40:40/10,matrix(P[[2]][,1]-P[[2]][,2],81),
add=T,levels=0,labex=c(),col='red')

LM <- lm(b~x+y,daten)
lines(c(-4,+4),c((LM$coefficients[["(Intercept)"]]+4*LM$coefficients[["x"]])/LM$coefficients[["y"]],(LM$coefficients[["(Intercept)"]]-4*LM$coefficients[["x"]])/LM$coefficients[["y"]]),col="blue")

library(e1071)
L <- svm(as.factor(b)~x+y,daten,kernel="linear",cost=100)
a <- rep(-80:80/20,161)
b <- rep(-80:80/20,rep(161,161))
P <- predict(L,data.frame("x"=a,"y"=b),type="probs")
contour(-80:80/20,-80:80/20,matrix(P,161),
add=T,levels=0,labex=c(),col='green')