All of the math is done initially using normal distributions, but I doubt that there is any detectable difference in practice between normal and uniform. To be precise, the only time I would expect to be able to see a difference between uniform and normal is in cases that have less than a dozen non-zeros per row on average in A. That is pretty pathological.
Having a non-zero mean could have bad effects if there were a huge number of non-zero elements, but probably has little practical impact. The ternary distribution is just a flop-saver as you suggest. A sparse ternary distribution worries me a bit, but the convergence guarantees are pretty compelling. A very sparse ternary distribution is probably very bad for the data we focus on because you have a significant chance of not using any element from some rows of A. On Fri, Dec 23, 2011 at 10:39 AM, Dmitriy Lyubimov <[email protected]>wrote: > or, rather, that they are of the same length. although any random > distribution actually should eventually converge on the same length > for sufficiently high dimensional vectors. > > also normal distribution would tend to keep vectors closer to > subspaces spanned by axes , thus probably ensuring better > orthogonality guarantee.. > > On Fri, Dec 23, 2011 at 10:33 AM, Dmitriy Lyubimov <[email protected]> > wrote: > > Ted, > > > > is Ternary matrix somehow better than uniform or normal for random > > projection? or it is just flops saving technique? > > > > Original study actually implied unit gaussian vectors, which i think > > is not quite exactly what we are doing with either technique. I think > > it is important that vectors are unitary, that way it better figures > > the subspace with major variances i think. >
