For example, palladium, platinum, silver and gold are considered to be precious metals, and silver, gold and copper considered to be coinage metals. Thus, we have:
metal
/ \
precious coinage
/ | \ \ / / \
/ | \ gold / \
palladium platinum silver copper
When calculating the semantic similarity between platinum and gold,
DiShIn starts by calculating the number of paths difference for all their common ancestors:
gold -> coinage -> metal
gold -> precious -> metal
platinum -> precious -> metal
gold -> precious
platinum -> precious
For metal we have two paths from gold and one from platinum, so we have a path difference of one.
For precious we have one path from each concept, so we have a path difference of zero.
Since their path difference is distinct, both common ancestors metal and precious are considered to be disjunctive common ancestors.
When calculating the semantic similarity between platinum and palladium,
DiShIn starts by calculating the number of paths difference for all their common ancestors:
palladium -> precious -> metal
platinum -> precious -> metal
palladium -> precious
platinum -> precious
For both metal and precious, we have only one path from each concept, so we have a path difference of zero for both common ancestors.
Thus, only the common ancestor precious (the most informative) is considered to be a disjunctive common ancestor.
Given that node-based semantic similarity measures are proportional to the average of the information content of their common disjunctive ancestors: metal and precious in case of platinum and gold; and precious in case of platinum and palladium, means that for DiShIn palladium and platinum are more similar than platinum and gold.
When calculating the semantic similarity between silver and gold,
DiShIn starts by calculating the number of paths difference for all their common ancestors:
gold -> coinage -> metal
gold -> precious -> metal
silver -> coinage -> metal
silver -> precious -> metal
gold -> precious
silver -> precious
gold -> coinage
silver -> coinage
As in the case of platinum and palladium, here all common ancestors have a path difference of zero, since silver and gold share the same relationships
and therefore have parallel interpretations.
Thus, only the most informative common ancestor precious or coinage is considered to be a disjunctive common ancestor.
This means that for DiShIn the similarity between silver and gold is greater or equal than the similarity between any other pair of the leaf concepts.
Thus, DiShIn does not penalize parallel interpretations as GraSM did.