Understanding the curse of dimensionality. Consider the following experiment: generate n data points with dimensionality k. Let each data point be generated using a uniform random number generator with values between 0 and 1. Now, for a given k, calculate r(k) = log10 (dmax(k) dmin(k) ) / dmin(k) where dmax(k) is the maximum distance between any pair of points and dmin(k) is minimum distance between any pair of points (you cannot use identical points to obtain the minimum distance of 0). Let k take each value from {1, 2, . . . , 99, 100}. Repeat each experiment multiple times to get stable values by averaging the quantities over multiple runs for each k.

Plot r(k) as a function of k for two different values of n; n {100, 1000}. Label and scale each axis properly to be able to make comparisons over different ns. Embed your final picture(s) in the file you are submitting for this assignment.

Discuss your observations and also compare the results to your expectations before you carried out the experiment