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.

采用归一化的非负模型（NNM）进行数据分析，其价值在于基于它对物品推荐的示例展现了满足三个标准的推荐系统应该具备的高预测力、计算可处理性和用户与物品的表达能力。