ex11_1_4.R

# exercise 11.1.4
rm(list=ls())
source("setup.R")
library(FNN)
source(file.path('Scripts', 'ex11_1_1.R'))
graphics.off()

# Number of neighbors
K = 200;

# x-values to evaluate the GMM
x <- seq(from=-10, to=10, length.out=100)

# Find the k nearest neighbors
res <- get.knnx(data=X, query=x, k=K)
i <- res$nn.index
D <- res$nn.dist

# Compute the density
density = 1/(rowSums(D)/K);

# Compute the average relative density
res <- get.knnx(data=X, query=X, k=K+1)
iX <- res$nn.index
DX <- res$nn.dist
densityX= 1/(rowSums(DX[,2:dim(DX)[2]])/K);
temp <- matrix(densityX[i[,2:dim(i)[2]]], nrow=dim(i)[1])
avg_rel_density=density/(rowSums(temp)/K);

# Plot KNN estimate of density
plot(x, density, main='KNN density', type='l');

# Plot KNN estimate of density
dev.new()
plot(x, avg_rel_density, main='KNN average relative density', type='l');