  User-provided multi-aspect evaluations manifest users' detailed feedback on
the recommended items and enable fine-grained understanding of their
preferences. Extensive studies have shown that modeling such data greatly
improves the effectiveness and explainability of the recommendations. However,
as ranking is essential in recommendation, there is no principled solution yet
for collectively generating multiple item rankings over different aspects. In
this work, we propose a directional multi-aspect ranking criterion to enable a
holistic ranking of items with respect to multiple aspects. Specifically, we
view multi-aspect evaluation as an integral effort from a user that forms a
vector of his/her preferences over aspects. Our key insight is that the
direction of the difference vector between two multi-aspect preference vectors
reveals the pairwise order of comparison. Hence, it is necessary for a
multi-aspect ranking criterion to preserve the observed directions from such
pairwise comparisons. We further derive a complete solution for the
multi-aspect ranking problem based on a probabilistic multivariate tensor
factorization model. Comprehensive experimental analysis on a large TripAdvisor
multi-aspect rating dataset and a Yelp review text dataset confirms the
effectiveness of our solution.
