Multilabel Classification With Ranking
the task seems very hard to understand what you want to achieve as you say that there several equally good representation for each data key... In other words, you say following?

kd1 = l1 + l2 + l3 + l4 + l5 + l6
kd1 = l1 + l7 + l8 + l9   l5 + l10
kd1 = l11 + l12 + l13 + l14 + l5 + l10
kd1 = ...