10 : The Johnson - Lindenstrauss Lemma ∗
نویسنده
چکیده
In this chapter, we will prove that given a set P of n points in IR, one can reduce the dimension of the points to k = O(ε−2 log n) and distances are 1 ± ε reserved. Surprisingly, this reduction is done by randomly picking a subspace of k dimensions and projecting the points into this random subspace. One way of thinking about this result is that we are “compressing” the input of size nd (i.e., n points with d coordinates) into size O(nε−2 log n), while (approximately) preserving distances.
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تاریخ انتشار 2007