2. In this problem, we would like to investigate another aspect of high- dimensional spaces or...

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2. In this problem, we would like to investigate another aspect of high- dimensional spaces or curse of dimensionality. Consider N data points uniformly distributed in a p-dimensional unit ball centered at the origin. Suppose we consider a nearest-neighbor estimate at the origin. Show that the median distance from the origin to the closest data point is given by (-(19)*)* d(p, N) = Evaluate d(p,N), for N=500, p=10, and see that d(10,500)>0.5. This means that it is likely that the closest point to the origin is more than halfway to the boundary. This means that in high dimensional spaces most data points are closer to the boundary. 2. In this problem, we would like to investigate another aspect of high- dimensional spaces or curse of dimensionality. Consider N data points uniformly distributed in a p-dimensional unit ball centered at the origin. Suppose we consider a nearest-neighbor estimate at the origin. Show that the median distance from the origin to the closest data point is given by (-(19)*)* d(p, N) = Evaluate d(p,N), for N=500, p=10, and see that d(10,500)>0.5. This means that it is likely that the closest point to the origin is more than halfway to the boundary. This means that in high dimensional spaces most data points are closer to the boundary.