Concepts are often described in terms of positive integer-valued attributes that are organized in a hierarchy. For example, cities can be described in terms of how many places there are of various types (e.g. nightlife spots, residences, food venues), where these places are organized in a hierarchy (e.g. a Portuguese restaurant is a type of food venue). This hierarchy imposes particular constraints on the values of related attributes—e.g. there cannot be more Portuguese restaurants than food venues. Moreover, knowing that a city has many food venues makes it less surprising that it also has many Portuguese restaurants, and vice versa. 

The proposed method attempts to characterize such concepts in terms of so-called contrastive antichains: particular kinds of subsets of their attributes and their values. It addresses the question of when a contrastive antichain is interesting, in the sense that it concisely describes the unique aspects of the concept, and this while duly taking into account the known attribute dependencies implied by the hierarchy. The proposed approach is capable of accounting from previously identified contrastive antichains, making iterative application possible. Besides the interestingness measure, this work aims to present  an algorithm that scales well in practice, and demonstrate the usefulness of the method. 

More details in:

• Anes Bendimerad, Jefrey Lijffijt, Marc Plantevit, Céline Robardet, Tijl de Bie. Contrastive antichains in hierarchies. SIGKDD 2019 , Aug 2019, Anchorage, Alaska, United States.
• https://www.kdd.org/kdd2019/