Critique graphs for catalogue navigation

Critique-based conversational recommender systems are be-coming common place, facilitating richer dialogues with the user than pure content-based or collaborative approaches. Most implementations of these systems combine similarity-based reasoning with constraints to enable users express preferences as critiques of products. Critiques are simple statements like "I like this product, but would prefer one that is less expensive". In this paper we exploit the fact that the repertoire of critiques available to the user is usually known ahead of interaction time to construct a critique graph representation of a catalogue. The critique graph pro- vides a formal basis for reasoning about the set of products that can be reached sing critiques from a given product. We introduce the concepts of product cover, support sets of products and catalogue cover. The latter is defined as a set of products from which all products in a catalogue can be reached using a specified best-case maximum number of critiques. We show that for the catalogues we considered, catalogue covers are typically small. We show that the sizes and distributions of product covers and support sets can be used to inform us of the structure of a catalogue and the challenges it would present for interactive navigation. We also propose the notion of a minimum catalogue cover as a set of "entry products" that ensure that all products in the catalogue can be reached by critiquing.