Conditional preference in recommender systems

•We find the conditional preference exists widely in recommender systems.•We propose to use quadratic polynomial to approximate conditional preference.•The proposed model is integrated into ListPMF and gets more satisfying results.

By investigating the users’ preferences in MovieLen dataset, we find that the conditional preference exists more widely in rating based recommender systems than imagined. Due to the high space complexity of the existing conditional preference representing models and the high computational complexity of the corresponding learning methods, conditional preference is seldom taken into consideration in the recommender systems. In this paper, we prove that the expressive ability of quadratic polynomial is stronger than that of linear function for conditional preference and propose to use quadratic polynomial to approximate conditional preference. Compared with the existing conditional preference model, the proposed model can save storage space and reduce learning complexity, and can be used in rating based recommender systems to efficiently process large amount of data. We integrate the proposed approximate conditional preference model into the framework of list-wise probabilistic matrix factorization (ListPMF), and verify this recommendation method on two real world datasets. The experimental results show that the proposed method outperforms other matrix factorization based methods.