text: We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ideally satisfy: high predictive power, computational tractability, and expressive representations of users and items. Expressive user and item representations are important in practice to succinctly summarize the pool of customers and the pool of items. In NNMs, user representations are expressive because each user's preference can be regarded as normalized mixture of preferences of stereotypical users. The interpretability of item and user representations allow us to arrange properties of items (e.g., genres of movies or topics of documents) or users (e.g., personality traits) hierarchically.
  @cite_12: Although Recommender Systems have been comprehensively analyzed in the past decade, the study of social-based recommender systems just started. In this paper, aiming at providing a general method for improving recommender systems by incorporating social network information, we propose a matrix factorization framework with social regularization. The contributions of this paper are four-fold: (1) We elaborate how social network information can benefit recommender systems; (2) We interpret the differences between social-based recommender systems and trust-aware recommender systems; (3) We coin the term Social Regularization to represent the social constraints on recommender systems, and we systematically illustrate how to design a matrix factorization objective function with social regularization; and (4) The proposed method is quite general, which can be easily extended to incorporate other contextual information, like social tags, etc. The empirical analysis on two large datasets demonstrates that our approaches outperform other state-of-the-art methods.
summary: Similarly, more general NMF-based models @cite_12 agree with NNM-based models in that they make prediction in terms of inner products of nonnegative vectors but they differ from NNM-based models through different interpretations and regularizations of those nonnegative vectors.