Dimension Reduction Methods with Application to ... - Rice University
Dimension Reduction Methods with Application to ... - Rice University
Dimension Reduction Methods with Application to ... - Rice University
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JL LEMMA: DASGUPTA AND GUPTA<br />
20 / 86<br />
Sketch of Proof<br />
◮ define f(x) = 1 √<br />
k<br />
xΓ, and y = √ k f(x)<br />
||x||<br />
◮ Let y j = xr j<br />
||x|| ∼ N(0, 1), and y2 j ∼ χ 2 1 <strong>with</strong> E(||y|| 2 ) = k<br />
◮ Let α 1 = k(1 + ɛ), and α 2 = k(1 − ɛ), then