  Recommender systems are frequently used in domains in which users express
their preferences in the form of graded judgments, such as ratings. If accurate
top-N recommendation lists are to be produced for such graded relevance
domains, it is critical to generate a ranked list of recommended items directly
rather than predicting ratings. Current techniques choose one of two
sub-optimal approaches: either they optimize for a binary metric such as
Average Precision, which discards information on relevance grades, or they
optimize for Normalized Discounted Cumulative Gain (NDCG), which ignores the
dependence of an item's contribution on the relevance of more highly ranked
items.
  In this paper, we address the shortcomings of existing approaches by
proposing the Graded Average Precision factor model (GAPfm), a latent factor
model that is particularly suited to the problem of top-N recommendation in
domains with graded relevance data. The model optimizes for Graded Average
Precision, a metric that has been proposed recently for assessing the quality
of ranked results list for graded relevance. GAPfm learns a latent factor model
by directly optimizing a smoothed approximation of GAP. GAPfm's advantages are
twofold: it maintains full information about graded relevance and also
addresses the limitations of models that optimize NDCG. Experimental results
show that GAPfm achieves substantial improvements on the top-N recommendation
task, compared to several state-of-the-art approaches. In order to ensure that
GAPfm is able to scale to very large data sets, we propose a fast learning
algorithm that uses an adaptive item selection strategy. A final experiment
shows that GAPfm is useful not only for generating recommendation lists, but
also for ranking a given list of rated items.
