[<<][math][>>][..]Thu Jun 6 14:46:17 EDT 2013

From [2]: ... under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. Is this related to the idea that the volume of a high dimensional sphere[3] is small compared to its bounding cube? I don't see the connection.. The basic problem seems to be that high-dimensional discrete-dimensional spaces are "very connected" in a way that is not immediately clear on an intuitive sense. Our usual 1,2,3-dimensional view is very particular, and doesn't generalize to larger numbers. [1] http://spin.atomicobject.com/2013/05/06/k-nearest-neighbor-racket/ [2] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1422 [3] http://en.wikipedia.org/wiki/N-sphere#n-ball

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