It is today accepted that matrix factorization models allow a high quality of rating prediction in recommender systems. However, a major drawback of matrix factorization is its static nature that results in a progressive declining of the accuracy of the predictions after each factorization. This is due to the fact that the new obtained ratings are not taken into account until a new factorization is computed, which can not be done very often because of the high cost of matrix factorization. In this paper, aiming at improving the accuracy of recommender systems, we propose a cluster-based matrix factorization technique that enables online integration of new ratings. Thus, we significantly enhance the obtained predictions between two matrix factorizations. We use finer-grained user biases by clustering similar items into groups, and allocating in these groups a bias to each user. The experiments we did on large datasets demonstrated the efficiency of our approach.
focus on users (and items) which have small rating profiles @cite_1 . They present an approximation method that updates the matrices of an existing model (previously generated by MF). The proposed and algorithms retrain the factor vector for the concerned user, or item, and keep all the other entries in the matrix unchanged. The time complexity of this method is @math , where @math is the given number of factors and @math the number of iterations. The whole factor vector of the user is retrained (i.e. his rating profile for all the items), which makes their solution more time consuming than ours ( @math , see Section ). They also not consider user biases, which might be very important for the accuracy of the predictions.
@cite_1
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We use a low-dimensional linear model to describe the user rating matrix in a recommendation system. A non-negativity constraint is enforced in the linear model to ensure that each user’s rating profile can be represented as an additive linear combination of canonical coordinates. In order to learn such a constrained linear model from an incomplete rating matrix, we introduce two variations on Non-negative Matrix Factorization (NMF): one based on the Expectation-Maximization (EM) procedure and the other a Weighted Nonnegative Matrix Factorization (WNMF). Based on our experiments, the EM procedure converges well empirically and is less susceptible to the initial starting conditions than WNMF, but the latter is much more computationally efficient. Taking into account the advantages of both algorithms, a hybrid approach is presented and shown to be effective in real data sets. Overall, the NMF-based algorithms obtain the best prediction performance compared with other popular collaborative filtering algorithms in our experiments; the resulting linear models also contain useful patterns and features corresponding to user communities. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. Regularized matrix factorization models are known to generate high quality rating predictions for recommender systems. One of the major drawbacks of matrix factorization is that once computed, the model is static. For real-world applications dynamic updating a model is one of the most important tasks. Especially when ratings on new users or new items come in, updating the feature matrices is crucial. In this paper, we generalize regularized matrix factorization (RMF) to regularized kernel matrix factorization (RKMF). Kernels provide a flexible method for deriving new matrix factorization methods. Furthermore with kernels nonlinear interactions between feature vectors are possible. We propose a generic method for learning RKMF models. From this method we derive an online-update algorithm for RKMF models that allows to solve the new-user new-item problem. Our evaluation indicates that our proposed online-update methods are accurate in approximating a full retrain of a RKMF model while the runtime of online-updating is in the range of milliseconds even for huge datasets like Netflix. Matrix approximation is a common model-based approach to collaborative filtering in recommender systems. Many relevant algorithms that fuse social contextual information have been proposed. They mainly focus on using the latent factor vectors of users and items to construct a low-rank approximation of the user-item rating matrix. However, due to data sparsity, it is difficult for current approaches to accurately learn every user item vector, which may cause low-quality recommendations for some users or items. But we implicitly detect some similar users or items based on the distance among the vectors. In this paper, we take advantage of the implicit similarity to improve matrix approximation. Borrowing parts of ideas from CodeBook Transfer, we propose a reconstructive method that compresses low-rank approximation into a cluster-level rating-pattern referred to as a codebook, and then constructs an improved approximation by expending the codebook. Experiments on real life datasets demonstrate our method improves the prediction accuracy of the state-of-the-art matrix factorization and social recommendation models.