Understanding Collaborative Filtering with Galois Connections
In this paper, we explain how Galois connection and related operators between sets of users and items naturally arise in user-item data for forming neighbourhoods of a target user or item for Collabora- tive Filtering. We compare the properties of these operators and their ap- plicability in simple collaborative user-to-user and item-to-item setting. Moreover, we propose a new neighbourhood-forming operator based on pair-wise similarity ranking of users, which takes intermediate place be- tween the studied closure operators and its relaxations in terms of neigh- bourhood size and demonstrates comparatively good Precision-Recall trade-off. In addition, we compare the studied neighbourhood-forming operators in the collaborative filtering setting against simple but strong benchmark, the SlopeOne algorithm, over bimodal cross-validation on MovieLens dataset.