> Unlike something like spectral clustering, it is the euclidean distance
> to the centers that is minimized. Thus K-Means will seek clusters that
> are regular in the flat euclidean space.
>
>    
Ok, that's right. Though I would argue that the distance measure
is not the only factor here. MeanShift also works with a euclidean
distance by using a Gaussian weighted density.
Here the difference is more in the objective then in the underlying 
distance.

>> Just know I have 4 plots of clustering algorithms on my desktop,
>> one of which I want to publish. Problem is: the clustering does not
>> agree with the classes, while the kmeans results do.
>> Now what? -_-
>>      
> That's a well known problem:
> http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.79.2501
>
>    
I'm tempted but would like to avoid going down that road ;)
>> Basically Shi/Malik multipy by the inverse diagonal from the right while
>> Jordan/Ng multiply by the square root form left and right - or something ;)
>>      
> But if you do it right, the two approaches solve the same problem, AFAIK.
>
>    
They lead to different generalized eigenvalue problems:
http://arxiv.org/pdf/0711.0189

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