How to plot non-linear decision boundaries with a grid in R?

Question

I find this particular graph in ISLR (Figure 2.13) or ESL very well done. I can\'t guess how the authors would have made this in R. I know how to get the orange and blue points

Answer 1

As I indicated in my comment, a solution was provided by @chl here on stats.stackexchange.com. Here it is, applied to your data set.

library(class)
set.seed(pi)
X <- t(replicate(1000, runif(2)))
g <- ifelse(apply(X, 1, sum) <= 1, 0, 1)
xnew <- cbind(rep(seq(0, 1, length.out=50), 50),
              rep(seq(0, 1, length.out=50), each=50))
m <- knn(X, xnew, g, k=15, prob=TRUE)
prob <- attr(m, "prob")
prob <- ifelse(m=="1", prob, 1-prob)
prob15 <- matrix(prob, 50)
par(mar=rep(3, 4))
contour(unique(xnew[, 1]), unique(xnew[, 2]), prob15, levels=0.5, 
        labels="", xlab='', ylab='', axes=FALSE, lwd=2.5, asp=1)
title(xlab=expression(italic('X')[1]), ylab=expression(italic('X')[2]), 
      line=1, family='serif', cex.lab=1.5)
points(X, bg=ifelse(g==1, "#CA002070", "#0571B070"), pch=21)
gd <- expand.grid(x=unique(xnew[, 1]), y=unique(xnew[, 2]))
points(gd, pch=20, cex=0.4, col=ifelse(prob15 > 0.5, "#CA0020", "#0571B0"))
box()

(UPDATE: I changed the colour palette because the blue/yellow/purple thing was pretty hideous.)

Answer 2

This was my silly attempt at approximation. Clearly the issues raised by @StephenKolassa are valid and not handled by this approximation.

myCurve1 = function (x)
  abs(x[[1]] * sin(x[[1]]) + x[[2]] * sin(x[[2]]))
myCurve2 = function (x)
  abs(x[[1]] * cos(x[[1]]) + x[[2]] * cos(x[[2]]))
myCurve3 = function (x)
  abs(x[[1]] * tan(x[[1]]) + x[[2]] * tan(x[[2]]))

tmp = function (myCurve, seed=99) {
  set.seed(seed)
  points = replicate(100, runif(2))
  colors = ifelse(apply(points, 2, myCurve) > 0.5, "orange", "blue")
  # Confound some
  swapInts = sample.int(length(colors), 6)
  for (i in swapInts) {
    if (colors[[i]] == "orange") {
      colors[[i]] = "blue"
    } else {
      colors[[i]] = "orange"
    }
  }
  gridPoints = seq(0, 1, 0.005)
  gridPoints = as.matrix(expand.grid(gridPoints, gridPoints))
  gridColors = vector("character", nrow(gridPoints))
  gridPch = vector("character", nrow(gridPoints))
  for (i in 1:nrow(gridPoints)) {
    val = myCurve(gridPoints[i, ])
    if (val > 0.505) {
      gridColors[[i]] = "orange"
      gridPch[[i]] = "."
    } else if (val < 0.495) {
      gridColors[[i]] = "blue"
      gridPch[[i]] = "."
    } else {
      gridColors[[i]] = "purple"
      gridPch[[i]] = "*"
    }
  }
  plot(x=gridPoints[ , 1], y=gridPoints[ , 2], col=gridColors, pch=gridPch)
  points(x=points[1, ], y=points[2, ], col=colors, lwd=2)
}

par(mfrow=c(1, 3))
tmp(myCurve1)
tmp(myCurve2)
tmp(myCurve3)