Nearest-neighbour distances and dimension

neighbours.R

library(FNN)

x1<-runif(5e4)
x2<-matrix(runif(5e4*2),ncol=2)
x10<-matrix(runif(5e4*10),ncol=10)
x100<-matrix(runif(5e4*100),ncol=100)

system.time(d1<-knn.dist(x1,k=1))
system.time(d2<-knn.dist(x2,k=1))
system.time(d10<-knn.dist(x10,k=1))
system.time(d100<-knn.dist(x100,k=1))


#coordinate-wise distance has triangular distribution with mean 1/3, variance 1/18

mean(d1/sqrt(1)/(1/3))
mean(d2/sqrt(2)/(1/3))
mean(d10/sqrt(10)/(1/3))
mean(d100/sqrt(100)/(1/3))