library(kknn)

auto <- read.table("http://azzalini.stat.unipd.it/Book-DM/auto.dat", header = TRUE)
attach(auto)

# code based on the file "Code regarding section 4.2" (copyright 2003, 2004, 2012 A.Azzalini and B.Scarpa)
y <- city.distance
x <- engine.size

# figure 4.3a from Azzalini & Scarpa (2012)
aaa <- kknn(y ~ x, train = data.frame(x = x, y = y), test = data.frame(x = x, y = y), k = 10)
plot(x, y, xlab = "Engine size (L)", ylab = "City distance (km/L)", pch = 16, cex = 1.5)
lines(sort(x), aaa$fitted.values[order(x)], col = 2, lwd = 2)

# figure 4.3b from Azzalini & Scarpa (2012)
bbb <- kknn(y ~ x, train = data.frame(x = x, y = y), test = data.frame(x = x, y = y), k = 60)
lines(sort(x), bbb$fitted.values[order(x)], col = 3, lwd = 2)


# curse of dimensionality
dist <- function(n, p) (1 - 0.5^(1/n))^(1/p)

P <- 10
N <- 10

distance <- matrix(NA, ncol = P, nrow = N)
for (i in 1:N)
  for (j in 1:P)
    distance[i, j] <- dist(i, j)

plot(distance[, 1], xlab = 'number of observations', ylab = 'distance', main = '1 dimension')
plot(distance[1, ], xlab = 'number of dimensions', ylab = 'distance', main = '1 observation')

heatmap(t(distance), Rowv = NA, Colv = NA, scale = 'none', xlab = 'observations', ylab = 'dimensions')