In your case, the rank of the Gram matrix is much smaller than the
number of samples. All this means that we need to add some kind of
regularization to it.
Bertrand
On 11/10/2011 04:00 AM, Alejandro Weinstein wrote:
> On Mon, Nov 7, 2011 at 12:32 PM, Jacob VanderPlas
> wrote:
>> I think, base
Hi Jacob,
Indeed, Isomap is a metric MDS, so you have the same hypothesis. A negative
eigenvalue should not happen, but one never knows.
As the eigenvalue only plays as a scaling factor, it is not too weird too
use a negative one in the embedding construction.
Cheers,
Matthieu
2011/11/7 Jacob V
On Mon, Nov 7, 2011 at 12:32 PM, Jacob VanderPlas
wrote:
> I think, based on this, that KernelPCA is correct as written, except
> that the arpack method should use which='LA' rather than which='LM'
> (thus ignoring any negative eigenvalues). This would fix Alejandro's
> problem. I'll make the ch
I dug around a bit, and found some info about kernel form in this document:
http://people.kyb.tuebingen.mpg.de/lcayton/resexam.pdf
MDS (on which Isomap is based) assumes a Euclidean distance matrix,
which can be shown to always yield a positive semidefinite kernel. In
the case of Isomap, the di
I looked closer: turns out arpack is actually up-to-date.
I think the bug is in the kernel pca code: eigsh should be called with
keyword which='LA' rather than which='LM'. The fit_transform routine
was finding three vectors, and then removing the one with a negative
eigenvalue.
Before making
Alejandro,
It looks like the problem can be traced back to the ARPACK eigensolver.
If you run the code with eigen_solver='dense', it works as expected.
Sometimes arpack does not converge to all the requested eigenvalues, and
I guess there's no error reported when that happens.
I tried perform
Hi:
I am observing an unexpected behavior of Isomap, related to the
dimensions of the transformed data. If I generate random data, say
1000 points each with dimension 10, and fit a transform using as a
parameter out_dim=3, the fitted data has dimension (1000, 3), as
expected. However, when I repea
