The ideal output would be the collection {{Mg, Ca, Sr} ,{Li, Na, K}}, as the elements in both of these families are predominantly found together in the families of the input collections. Variations on these (for instance inclusion of Cl or Hg) are regarded as random noise, introduced in any of the previous steps, that is in the optimisation of sequences of elements (Methods 6.3), or in the computer vision pipeline (Methods 6.7). By decrease of variability we mean the removal of such noise. It is however also desired to preserve both families, in what is regarded here as preserving diversity.