A User-Item Relevance Model for Log-based Collaborative Filtering

Abstract. Implicit acquisition of user preferences makes log-based collaborative filtering favorable in practice to accomplish recommendations. In this paper, we follow a formal approach in text retrieval to re-formulate the problem. Based on the classic probability ranking principle, we propose a probabilistic user-item relevance model. Under this formal model, we show that user-based and item-based approaches are only two different factorizations with different independence assumptions. Moreover, we show that smoothing is an important aspect to estimate the parameters of the models due to data sparsity. By adding linear interpolation smoothing, the proposed model gives a probabilistic justification of using TF×IDF-like item ranking in collaborative filtering. Besides giving the insight understanding of the problem of collaborative filtering, we also show experiments in which the proposed method provides a better recommendation performance on a music play-list data set.