[mlpack] Fwd: Dissimilar matrices in multi-dimensional scaling

[Dhawal Arora]

---------- Forwarded message ----------
From: Dhawal Arora <d.p.arora1 at gmail.com>
Date: Sat, Mar 7, 2015 at 1:30 AM
Subject: Re: [mlpack] Dissimilar matrices in multi-dimensional scaling
To: Ryan Curtin <ryan at ratml.org>


Hi Ryan,

Sorry couldn't keep up with the superLU lately. Its kinda going a bit slow
here right now as my exams are going on. Sad that mlpack couldn't make it
through this time, badly wanted to complete this manifold stuff this
summer. But i still would like to contribute. Had a look at the metrics,
using mahalonobis for euclidean distance although working to implement some
other distances too.

following this paper(for MDS) although i've read the paper on the ideas
page:
http://www.math.uwaterloo.ca/~aghodsib/courses/f06stat890/readings/tutorial_stat890.pdf

a proof(pg 16) in his paper helped me switch to above implementation.
http://www.lcayton.com/resexam.pdf

Also Is it over with eigs_sym_pair() ? Could you please tell where
eigs_sym_pair() would fit in here? Right now in MDS i am using eigs_pair
and eigs_sym of armadillo.
Also not getting any clear idea or paper for non-metric MDS. If you could
help on this. Will then probably try testing it in comparison to scikit.

Thanks.

Regards,
Dhawal Arora.

On Mon, Feb 16, 2015 at 10:29 PM, Ryan Curtin <ryan at ratml.org> wrote:

> On Mon, Feb 16, 2015 at 06:08:31AM +0530, Dhawal Arora wrote:
> > Hi Ryan,
> >
> > I am going through the arpack_wrapper and other armadillo source, its a
> bit
> > abstruse but will probably figure it out after sometime.
> > So meanwhile i've started implementing multi-dimensional scaling before
> > generlized eigenvectors get wrapped. Should i continue with it?
>
> Sure, you can assume that an eigs_sym_pair() function will eventually be
> available, which will solve the eigenproblem Ax = Bx\lambda and return
> some eigenvalues \lambda and some eigenvectors x.  The API will look
> like a cross between eig_pair() and eigs_sym().
>
> I'll keep you updated as the SuperLU wrapper becomes closer to done.
> Today I think I figured out how to wrap it correctly (it's ugly, but I
> think it works), and in the next few days I'll build the rest of the
> wrapper in order to provide lu() and solve(), which will then enable me
> to write eigs_sym_pair().  It's a long dependency chain...
>
> > I guess i've seen simple eigenvalue and eigenvectors already being
> > used in PCA so can work them through in MDS too. And regarding
> > dissimilar matrices, should i go with including them in MDS or i am
> > thinking to probably create them separately in core/math as these
> > might include euclidean, manhattan, maximum and a bunch of other
> > distances. Thanks.
>
> Are you able to use the distances we already have in
> src/mlpack/core/metrics/?  Or do you mean something else?
>
> You should be able to templatize your implementation so that it can work
> with any distance metric.
>
> Thanks,
>
> Ryan
>
> --
> Ryan Curtin    |
> ryan at ratml.org | "Death is the road to awe."
>
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