Author: Sune Fischer
Date: 04:31:48 12/09/01
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On December 09, 2001 at 06:57:28, David Rasmussen wrote: >>About linear independence: If you pick 768 random vectors of length 64, then >>they span the whole space with probability close to 1 (I haven't exactly >>computed that, and I don't intend to do it.) > >Sure, but that's not the only thing that is important. We want every vector be >the linear combination of as many basis vectors as possible. If you imagine it >in three dimensions with a plain orthonormal basis, we don't want the vectors to >lie close to the axes. We want them scattered equally about. If you change just one bit, you are orthonormal to the rest and that is enough, closeness is not related to spanning at all. >>As I said before, if your Hamming criterion works better than pure random >>numbers, that's fine with me; I would just like to understand the reason why. >>Always the inquisitive mind... >> > >I also would like to know _exactly_ why it works better. As I have said before, >no one really knows the exact full set of criterions we want for our vectors. I suggest we test it, not for 64 bits but for 16-20 bits, then we will cetainly see collisions. How do you make those Hamming optimizers? Do you just generate a lot of keys until they satisfy some requirement? What you this requirement be for 20 bit keys? >>Actually, the problem of hash codes is a little bit more complicated, since we > >Exactly. > >>also want to avoid minor collisions, i.e., different positions occupying the >>same spot in the transposition table. Since usually the first 20 bits of the >>hash key determine that position, we would like to avoid linear independence >>also for small sets of these truncated vectors. Have you tried applying the >>Hamming criterion to these leading bits? Actually I use the mod operator, so I am not 1-bit sensitive for indexing. -S.
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