[SciPy-user] PyEM: custom (non-Euclidean) distance function?

[Emanuele Olivetti]

David Cournapeau wrote:
> On Tue, Mar 17, 2009 at 1:46 AM, Emanuele Olivetti
> <emanuele at relativita.com> wrote:
>   
>> You are right. I'm coming from K-means (MacKay's book) and
>> moving to GMM, that's why I had in mind custom distances.
>>     
>
> Note that GMM is what is called soft kmean in MacKay's book. You can
> use other distances for kmeans, and other kind of soft-kmeans - but as
> said by Josef, I am more puzzled by the idea of non euclidean distance
> in the EM context, because of the inherent probabilistic view. Because
> of the probabilities, there is no obvious interpretation in distance
> anymore (it is not an argmin_c ||x-c|| for each point x).
>
> There are soft kmeans algorithms with non euclidean distances, but not
> in a probabilistic framework - at least I am not aware of any.
>
>   

I heard about kernel GMM, which could be of interest for this thread:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.2779
they seems to mix data projection and GMM in a single step.

cheers,

Emanuele