On Sun, Mar 25, 2012 at 11:56:31PM +0200, Andreas wrote:
> As far as I can see, your groups are "KMeans + Ward" and "rest".
> I don't know how ward works but looking at the lena example,
> the clusters don't seem to be convex.

But you are looking in the wrong space: the physical space, and not the
feature space.

> >>> But if you do it right, the two approaches solve the same problem, AFAIK.

> >> They lead to different generalized eigenvalue problems:
> >> http://arxiv.org/pdf/0711.0189

> > Yes (that's exactly the reference that I had in mind), but they should
> > minimize the same energy, right?

> Skimming the tutorial, I am not sure what the answer to that question is.
> I think they are both relaxations of the normalized cuts problem,
> but lead to different solutions in gerneral.

Back when I looked at that in details, I convinced myself that they were
solving the same problem, but one was using a positive-definite eigen
value problem, and the other a general one. The positive-definite problem
is much easier to solve, and more stable numerically.

> The tutorial suggests using Shi/Malik but since both are in
> use in the literature, I thought it would be nice to have them both.

My understanding is that the non-positive-definite formulation really
shouldn't be used, as it is slower and less stable.

G

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