agglomerative clustering - cluster update

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Do the values of each cluster get updated after each iteration ? If yes, how is it updated ? Mean ? What if I have a custom function ? What if I need to update it by addition instead of mean ? Like size of cluster.
I am using watershed to initialize agglomerative clustering and I want to take into account the sizes of the cluster when i merge it i.e. the cluster size is in my custom function.

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