Sapling Similarity outperforms other local similarity metrics in collaborative filtering

Many bipartite networks describe systems where a link represents a relation between a user and an item. Measuring the similarity between either users or items is the basis of memory-based collaborative filtering, a widely used method to build a recommender system with the purpose of proposing items to users. When the edges of the network are unweighted, traditional approaches allow only positive similarity values, so neglecting the possibility and the effect of two users (or two items) being very dissimilar. Here we propose a method to compute similarity that allows also negative values, the Sapling Similarity. The key idea is to look at how the information that a user is connected to an item influences our prior estimation of the probability that another user is connected to the same item: if it is reduced, then the similarity between the two users will be negative, otherwise it will be positive. Using different datasets, we show that the Sapling Similarity outperforms other similarity metrics when it is used to recommend new items to users.