On Mon, Apr 25, 2011 at 4:08 PM, Ted Dunning <[email protected]> wrote:
> I thought that for a moment as well, but now I think not. > > The trivial counter example consists of one element for each single > component unit vector e_i. The SVD of this has unit singular values and > the > eigenvectors are just the e_i themselves. After transformation, all values > are still in the positive orthant. > Still in the positive orthant is cutting things pretty close: all vectors are literally *on the border* of the positive orthant, and random hyperplanes will separate these vectors. > I may have misunderstood what you are suggesting, but I don't think that > LSH > could distribute the values into other orthants. > No, LSH won't distribute them, by itself. > It may be that in practice that SVD will scatter data into many orthants, > but I suspect it will not spread the data as widely as LSH assumptions > would > like. Maybe you're right - raw SVD vs PCA (where the means are also subtracted off) is probably the distinction to draw here. -jake
