All Questions

Let $X = \{v_1,\ldots,v_n\}$ be a set of vectors non-zero vectors $v_i \ge 0$ and such that the vectors are pairwise linear independent. Define a function on this set $X$: $$d(v,w) = 1-\frac{2 \...

Consider the Johnson-Lindenstrauss lemma in the case where we can assume the $n$ input points $x_i$ in $\mathbb{R}^d$ are actually located on the sphere $$S^{d-1}(r):=\{u=(u_1,\ldots,u_{d}): u_1^2+\...

Consider the following standard formulation of the Johnson-Lindenstrauss lemma: Lemma (JL). For any $0<\epsilon < 1$ and any integer $n$, let $k$ be a positive integer such that $k\geq C\...