Hierarchical Clustering Using Ordinal Queries 1 Motivation

We have seen equivalence query, split query and merge query. In this lecture, we want to talk about ordinal query and hierarchical clustering in Zadeh and Kempe [1]. For a set of elements, we can cluster the elements that are “similar to each other”. Moreover, for a same set of elements, we can have different way of clustering based on smaller concept or broader concept. For example, cat and dog are more similar to each other than zebra because cat and dog can be pets but zebra can not. Yet, {cat, dog and zebra} are more similar to each other than {tree and flowers} since the first group is animal and the second group is plant. Both group falls into category of creature. Hence, we can cluster the set {cat, dog, zebra, tree, flower} as {(cat,dog),(zebra),(tree,flower)} or {(cat,dog,zebra),(tree,flower)}. This forms a hierarchical clustering tree: (( (cat, dog), zebra ) , (tree, flower) ) .