Thanks heer2351 and Sendai. Indeed there are 6 different centreconfigurations, the ones you gave complete the picture. You can also see this with paper&pencil.
Quote:
Originally Posted by heer2351
@Sendai
What values for Ein do you get when running your algorithm with Lloyds centers?
I think I am still somewhere off the track

With this 4point example the only options for Ein are: 0, 0.25, 0.5
Anything else you get, you know your code has a bug.
I have not tried it with my code, but Sendai's results seem correct. So you should get Ein =0 for the centres that have 1/3 or 2/3 in them (when the clusters are 31 points) and Ein = 0.5 when the centres have 1/2 in them (the case were the clusters are 22points)
I also think that it might be impossible to get Ein= 0.25 for any centre configuration, providing that the weights are chosen optimally (i.e., using the pseudo inverse method). So you either make no mistakes, or 2 points are misclassified.