Rank and relevance in novelty and diversity metrics for recommender systems

The Recommender Systems community is paying increasing attention to novelty and diversity as key qualities beyond accuracy in real recommendation scenarios. Despite the raise of interest and work on the topic in recent years, we find that a clear common methodological and conceptual ground for the evaluation of these dimensions is still to be consolidated. Different evaluation metrics have been reported in the literature but the precise relation, distinction or equivalence between them has not been explicitly studied. Furthermore, the metrics reported so far miss important properties such as taking into consideration the ranking of recommended items, or whether items are relevant or not, when assessing the novelty and diversity of recommendations. We present a formal framework for the definition of novelty and diversity metrics that unifies and generalizes several state of the art metrics. We identify three essential ground concepts at the roots of novelty and diversity: choice, discovery and relevance, upon which the framework is built. Item rank and relevance are introduced through a probabilistic recommendation browsing model, building upon the same three basic concepts. Based on the combination of ground elements, and the assumptions of the browsing model, different metrics and variants unfold. We report experimental observations which validate and illustrate the properties of the proposed metrics.