Cross-Space Affinity Learning with Its Application to Movie Recommendation

In this paper, we propose a novel cross-space affinity learning algorithm over different spaces with heterogeneous structures. Unlike most of affinity learning algorithms on the homogeneous space, we construct a cross-space tensor model to learn the affinity measures on heterogeneous spaces subject to a set of order constraints from the training pool. We further enhance the model with a factorization form which greatly reduces the number of parameters of the model with a controlled complexity. Moreover, from the practical perspective, we show the proposed factorized cross-space tensor model can be efficiently optimized by a series of simple quadratic optimization problems in an iterative manner. The proposed cross-space affinity learning algorithm can be applied to many real-world problems, which involve multiple heterogeneous data objects defined over different spaces. In this paper, we apply it into the recommendation system to measure the affinity between users and the product items, where a higher affinity means a higher rating of the user on the product. For an empirical evaluation, a widely used benchmark movie recommendation data set—MovieLens—is used to compare the proposed algorithm with other state-of-the-art recommendation algorithms and we show that very competitive results can be obtained.