[R] SVM classification based on pairwise distance matrix

[Steve Lianoglou]

Hi,

On Thu, Oct 21, 2010 at 12:12 PM, Martin Tomko <martin.tomko at geo.uzh.ch> wrote:
> Hi Steve,
> tahnks for the hints and clarifications.
> Unfortunately, I will not be able to use the approach you suggest, The
> distances I generate are distances between VERY large matrices (say
> 100000x100000 and more) each  of different dimensions (not necessarily
> square either), and there is no significance in terms of column properties,
> they are basically graphs of sort.
>
> Is there a way out with the SVM, or I just forget that?

Well, it's not clear to me what type of data you are working with. You
say they are "graphs of sort." There are "principled" ways of working
with graphs in SVMs -- namely using "graph kernels". You can find
information about them if you run through google (Karsten Borgwadt
does a lot of work in this area). Unfortunately, I don't think there
are any public-domain implementations out there for you to consume
easily.

But still -- you're able to calculate a distance metric over your data
-- how are you doing that?

Here's a shot at the dark, and probably not so correct, but read at
your own risk:

What if you try to create a kernel matrix by plugging your distance
metric into the appropriate place from something like an RBF kernel
function. For instance, the value of the RBF kernel between two points
is:

exp(-|X_1 - X_2|^2 / sigma^2)

What if you plugged your distance measure between samples X_1 and X_2
into the |X_1 - X_2| slot and kept the rest the same?

You have to verify that this is a valid kernel (gram) matrix -- I
think it just needs to be symmetric positive definite. See a quick
review here:
http://www.support-vector.net/icml-tutorial.pdf

Now your just left to figure out how to use ksvm (from kernlab) with
kernel matrices and maybe you have something that can work.

-- 
Steve Lianoglou
Graduate Student: Computational Systems Biology
 | Memorial Sloan-Kettering Cancer Center
 | Weill Medical College of Cornell University
Contact Info: http://cbio.mskcc.org/~lianos/contact