PMD: An Optimal Transportation-Based User Distance for Recommender Systems

Collaborative filtering predicts a user’s preferences by aggregating ratings from similar users and thus the user similarity (or distance) measure is key to good performance. Existing similarity measures either consider only the co-rated items for a pair of users (but co-rated items are rare in real-world sparse datasets), or try to utilize the non-co-rated items via some heuristics. We propose a novel user distance measure, called Preference Mover’s Distance (PMD), based on the optimal transportation theory. PMD exploits all ratings made by each user and works even if users do not share co-rated items at all. In addition, PMD is a metric and has favorable properties such as triangle inequality and zero self-distance. Experimental results show that PMD achieves superior recommendation accuracy compared with the state-of-the-art similarity measures, especially on highly sparse datasets.