Curse of dimensionality

curse-of-dimensionality.py

import numpy
import pylab

def sample(d=2, N=1000):
    return [[uniform(0., 1.) for i in range(d)] for _ in range(N)]

def corner_count(points):
    return mean([any([(d < .01 or d > .99) for d in p]) for p in points])

def go(Ds=range(1,200)):
    plot(Ds, [corner_count(sample(d)) for d in Ds])

curse-of-dimensionality.R

d <- 1:200
N <- 1000
dat <- lapply(d, function(i) replicate(i, runif(N)))

nout <- function(m) mean(apply(m, 1, function(i) any(i < 0.01 | i > 0.99)))

res <- sapply(dat, nout)

plot(res, type = "l",
     xlab = "Number of dimensions",
     ylab = "Proportion of 1% outliers",
     main = "Curse of Dimensionality")
grid()