Analogy in Recommendation. Numerical vs. Ordinal: a Discussion

The paper investigates the use of analogical reasoning for recommendation purposes. More particularly, we address the problem of predicting missing ratings on the basis of known ones. After discussing the differences with another recently experimented approach based on analogical proportions, a new analogical approach is proposed. It relies on the intuition that "the rating of user u for item i is to the rating of user v for item i as the rating of user u for item j is to the rating of user v for item j". This leads to algorithms yielding results close to the ones of state-of-the art approaches, when the ratings are regarded as numerical quantities. This is due to the fact that these latter approaches embed an estimation process that is implicitly close to analogy, as discussed in this paper. An analogical approach is also outlined and briefly discussed when the ratings are supposed to have an ordinal meaning only.