Once again, we should be able to verify that the Equation (7)
corresponds to the cost Cv,p(`(v) | `) defined by Equation (3)
in the case that the cluster-label similarity function H is the
set-intersection function I. In fact, for the problems defined by
Equation (3) we always have hj +mj = 1. However, since we
do not know how to take advantage of the additional structure
hj + mj = 1 we just formulate Problem 4 in its generality.