Rで最小二乗法による線形識別

PRML図4.4のように、二乗和誤差の最小化では、適切に線形識別できないことを示します。

library(MASS)
frame()
par(mfrow=c(1,2))
set.seed(0)
x<-mvrnorm(40, c(0,1), matrix(c(2, 1.9, 1.9, 2), 2))
d1<-as.data.frame(cbind(x, 1, 1, 0))
x<-mvrnorm(40, c(2,0), matrix(c(2, 1.9, 1.9, 2), 2))
d1<-rbind(d1, as.data.frame(cbind(x, 2, 0, 1)))
x<-mvrnorm(10, c(7,-7), matrix(c(.2, 0, 0, .2), 2))
d2<-rbind(d1, as.data.frame(cbind(x, 2, 0, 1)))
names(d1)<-c("x1","x2","class","t1","t2")
names(d2)<-c("x1","x2","class","t1","t2")
 
doplot<-function(d) {
    xrange<-c(-4, 8)
        yrange<-c(-8, 4)
        base<-function(x1, x2) {
                (cbind(1, x1, x2))   # w0をバイアス項とするためφ0=1
        }
        phi<-base(d$x1, d$x2)
        t<-cbind(d$t1, d$t2)
        w<-solve(t(phi) %*% phi) %*% t(phi) %*% t
        print(w)
        estimate<-function(x1, x2, index){
                (t(w) %*% t(base(x1, x2)))[index,]
        }
        x1<-seq(-4,8,.1)
        x2<-seq(-8,4,.1)
        t1<-outer(x1, x2, estimate, 1)
        t2<-outer(x1, x2, estimate, 2)
        plot(d$x1, d$x2, col=d$class,xlim=xrange,ylim=yrange)
        contour(x1,x2,t2-t1,xlim=xrange,ylim=yrange,add=T)
}
 
doplot(d1)
doplot(d2)