Matrix factorization has found incredible success and widespread application as a collaborative filtering based approach to recommendations. Unfortunately, incorporating additional sources of evidence, especially ones that are incomplete and noisy, is quite difficult to achieve in such models, however, is often crucial for obtaining further gains in accuracy. For example, additional information about businesses from reviews, categories, and attributes should be leveraged for predicting user preferences, even though this information is often inaccurate and partially-observed. Instead of creating customized methods that are specific to each type of evidences, in this paper we present a generic approach to factorization of relational data that collectively models all the relations in the database. By learning a set of embeddings that are shared across all the relations, the model is able to incorporate observed information from all the relations, while also predicting all the relations of interest. Our evaluation on multiple Amazon and Yelp datasets demonstrates effective utilization of additional information for held-out preference prediction, but further, we present accurate models even for the cold-starting businesses and products for which we do not observe any ratings or reviews. We also illustrate the capability of the model in imputing missing information and jointly visualizing words, categories, and attribute factors.
The idea of using low-dimensional vectors as latent factors has found widespread use in recommendation systems. The task of suggesting products items to users is traditionally viewed as matrix completion where the sparse rating matrix with users as rows and items as columns is to be completed with predicted ratings. show how Singular Value Decomposition (SVD) can be used to decompose the rating matrix into low rank feature matrices to reduce dimensions of the rating matrix. This gave rise to the widely used matrix factorization techniques for predicting ratings @cite_9 in which the user and item factors capture the similarities amongst them. Conventional matrix factorization techniques predict ratings directly as the dot product of the factors of the user and the item, and use regularized least-squares as the loss function to optimize. Our model here however uses the interpretation of matrix factorization @cite_18 and uses the sigmoid function with log-likelihood as it is a generalization of PCA to binary matrices @cite_14 .
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As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearest neighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Principal component analysis (PCA) is a commonly applied technique for dimensionality reduction. PCA implicitly minimizes a squared loss function, which may be inappropriate for data that is not real-valued, such as binary-valued data. This paper draws on ideas from the Exponential family, Generalized linear models, and Bregman distances, to give a generalization of PCA to loss functions that we argue are better suited to other data types. We describe algorithms for minimizing the loss functions, and give examples on simulated data. Many existing approaches to collaborative filtering can neither handle very large datasets nor easily deal with users who have very few ratings. In this paper we present the Probabilistic Matrix Factorization (PMF) model which scales linearly with the number of observations and, more importantly, performs well on the large, sparse, and very imbalanced Netflix dataset. We further extend the PMF model to include an adaptive prior on the model parameters and show how the model capacity can be controlled automatically. Finally, we introduce a constrained version of the PMF model that is based on the assumption that users who have rated similar sets of movies are likely to have similar preferences. The resulting model is able to generalize considerably better for users with very few ratings. When the predictions of multiple PMF models are linearly combined with the predictions of Restricted Boltzmann Machines models, we achieve an error rate of 0.8861, that is nearly 7 better than the score of Netflix's own system.