I have a variant of k-means, where the points are reassigned incrementally and I have a few questions about it.
Each time we reassign a point (we move the point from cluster $C_1 $to $C_2$), we recompute both the centroids of $C_1 $and $C_2$. The centroid of a cluster $C$ is computed as the mean of the points in $C$.
1) Why does it produces k non-empty clusters ?
2) Can you find an exemple where a different order of processing the input points gives different clusterings ?
Thanks for your help !