I agree with JunWen, I am not entirely certain why would one want to use an asymmetric dissimilarity measure ?

on anand's idea I would like to point out, in the normalized cut, the similarity and dissimilarity between clusters turned out to be symmetric, and maximizing one was equivalent to the other.

for the average cut and the average association cut, one of the two measures dominate, and you get clustering which is appropriately biased.

so my guess is, if you can find a similarity measure that is linearly related to the dissimilartity measure, you will save yourself the trouble of selecting a regularization term (the penalty scaling factor) and get good EM performance too.