As alluded previously, you need to find a way to compute the centroid by
minimizing the sum of squared distances to a given set of points within each
cluster. However, it is true that re-projecting the euclidean mean to the
sphere would approximate well the theoretical solution in most cases.
A standard alternative to k-means is Von Mises-Fisher distribution.
Bertrand
----- Mail original -----
> De: "Vince Fernando" <y...@vincefernando.co.uk>
> À: math...@mblondel.org, scikit-learn-general@lists.sourceforge.net
> Envoyé: Jeudi 24 Janvier 2013 09:55:46
> Objet: Re: [Scikit-learn-general] K means on a sphere
> Are there any theoretical problems if one uses the great circle
> (orthodromic) distance on a sphere in k-means or any other
> clustering algorithm?
> vince
> On 24 January 2013 07:11, Mathieu Blondel < math...@mblondel.org >
> wrote:
> > On Thu, Jan 24, 2013 at 9:24 AM, Gael Varoquaux
>
> > < gael.varoqu...@normalesup.org > wrote:
>
> > > Yes, there is a massive difference in amount of work and
> > > performance when
>
> > > you try to replace the Euclidean distance. Amongst other
> > > problems,
> > > the
>
> > > mean is no longer the sum divided by the number of points, but
> > > the
>
> > > Frechet mean, which requires solving an optimization problem.
>
> > Indeed, if you replace the Euclidean distance, you also need to
> > change
>
> > the averaging.
>
> > If you use the Manhattan distance, the averaging becomes the
> > median.
>
> > Mathieu
>
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