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_9: Probabilistic Latent Semantic Indexing is a novel approach to automated document indexing which is based on a statistical latent class model for factor analysis of count data. Fitted from a training corpus of text documents by a generalization of the Expectation Maximization algorithm, the utilized model is able to deal with domain specific synonymy as well as with polysemous words. In contrast to standard Latent Semantic Indexing (LSI) by Singular Value Decomposition, the probabilistic variant has a solid statistical foundation and defines a proper generative data model. Retrieval experiments on a number of test collections indicate substantial performance gains over direct term matching methods as well as over LSI. In particular, the combination of models with different dimensionalities has proven to be advantageous.
  @cite_14: We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model.
  @cite_3: 
summary: In recommendation we are interested in the co-occurence of pairs @math of users @math and items @math . Depending on the application, @math may be interpreted as , , etc. In , @cite_3 @cite_9 (and similarly in their extension @cite_14 ) we model @math as random variable with distribution P [u,i] = k=1 ^K ; P [u|k] ; P [i|k]. Hence, @math is expressed as a inner product of two vectors: @math and @math . This is reminiscent of where we expressed the probability of the event in terms of the inner product between @math and @math . Therefore, one half of the inner product agrees with the identity as both @math and @math are probability distributions. However, aspect models and NNMs disagree on the other half (i.e., @math ) because @math is constrained through the existence of @math such that @math . More importantly however, the difference between aspect models and NNMs lies in the different interpretations of @math and @math on the one hand and @math and @math on the other hand.