text: Probabilistic graphic model is an elegant framework to compactly present complex real-world observations by modeling uncertainty and logical flow (conditionally independent factors). In this paper, we present a probabilistic framework of neighborhood-based recommendation methods (PNBM) in which similarity is regarded as an unobserved factor. Thus, PNBM leads the estimation of user preference to maximizing a posterior over similarity. We further introduce a novel multi-layer similarity descriptor which models and learns the joint influence of various features under PNBM, and name the new framework MPNBM. Empirical results on real-world datasets show that MPNBM allows very accurate estimation of user preferences.
  @cite_18: Neighborhood-based algorithms are frequently used modules of recommender systems. Usually, the choice of the similarity measure used for evaluation of neighborhood relationships is crucial for the success of such approaches. In this article we propose a way to calculate similarities by formulating a regression problem which enables us to extract the similarities from the data in a problem-specific way. Another popular approach for recommender systems is regularized matrix factorization (RMF). We present an algorithm -- neighborhood-aware matrix factorization -- which efficiently includes neighborhood information in a RMF model. This leads to increased prediction accuracy. The proposed methods are tested on the Netflix dataset.
  @cite_8: The collaborative filtering approach to recommender systems predicts user preferences for products or services by learning past user-item relationships. In this work, we propose novel algorithms for predicting user ratings of items by integrating complementary models that focus on patterns at different scales. At a local scale, we use a neighborhood-based technique that infers ratings from observed ratings by similar users or of similar items. Unlike previous local approaches, our method is based on a formal model that accounts for interactions within the neighborhood, leading to improved estimation quality. At a higher, regional, scale, we use SVD-like matrix factorization for recovering the major structural patterns in the user-item rating matrix. Unlike previous approaches that require imputations in order to fill in the unknown matrix entries, our new iterative algorithm avoids imputation. Because the models involve estimation of millions, or even billions, of parameters, shrinkage of estimated values to account for sampling variability proves crucial to prevent overfitting. Both the local and the regional approaches, and in particular their combination through a unifying model, compare favorably with other approaches and deliver substantially better results than the commercial Netflix Cinematch recommender system on a large publicly available data set.
  @cite_6: 
  @cite_3: This paper focuses on developing effective and efficient algorithms for top-N recommender systems. A novel Sparse Linear Method (SLIM) is proposed, which generates top-N recommendations by aggregating from user purchase rating profiles. A sparse aggregation coefficient matrix W is learned from SLIM by solving an 1-norm and 2-norm regularized optimization problem. W is demonstrated to produce high quality recommendations and its sparsity allows SLIM to generate recommendations very fast. A comprehensive set of experiments is conducted by comparing the SLIM method and other state-of-the-art top-N recommendation methods. The experiments show that SLIM achieves significant improvements both in run time performance and recommendation quality over the best existing methods.
  @cite_5: Recommender systems provide users with personalized suggestions for products or services. These systems often rely on Collaborating Filtering (CF), where past transactions are analyzed in order to establish connections between users and products. The two more successful approaches to CF are latent factor models, which directly profile both users and products, and neighborhood models, which analyze similarities between products or users. In this work we introduce some innovations to both approaches. The factor and neighborhood models can now be smoothly merged, thereby building a more accurate combined model. Further accuracy improvements are achieved by extending the models to exploit both explicit and implicit feedback by the users. The methods are tested on the Netflix data. Results are better than those previously published on that dataset. In addition, we suggest a new evaluation metric, which highlights the differences among methods, based on their performance at a top-K recommendation task.
  @cite_15: Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive knearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.
  @cite_13: 
  @cite_12: Recommender systems based on collaborative filtering predict user preferences for products or services by learning past user-item relationships. A predominant approach to collaborative filtering is neighborhood based ("k-nearest neighbors"), where a user-item preference rating is interpolated from ratings of similar items and or users. We enhance the neighborhood-based approach leading to substantial improvement of prediction accuracy, without a meaningful increase in running time. First, we remove certain so-called "global effects" from the data to make the ratings more comparable, thereby improving interpolation accuracy. Second, we show how to simultaneously derive interpolation weights for all nearest neighbors, unlike previous approaches where each weight is computed separately. By globally solving a suitable optimization problem, this simultaneous interpolation accounts for the many interactions between neighbors leading to improved accuracy. Our method is very fast in practice, generating a prediction in about 0.2 milliseconds. Importantly, it does not require training many parameters or a lengthy preprocessing, making it very practical for large scale applications. Finally, we show how to apply these methods to the perceivably much slower user-oriented approach. To this end, we suggest a novel scheme for low dimensional embedding of the users. We evaluate these methods on the netflix dataset, where they deliver significantly better results than the commercial netflix cinematch recommender system.
summary: With respect to NBM, researches have mainly focused on computation schemes @cite_6 and neighbor selection strategies @cite_5 . also serves as the basis for neighbor selection, thus we concentrate upon in this paper. Generally, there are two main approaches to compute . One introduces different kinds of correlation coefficients as @cite_6 , such as Pearson and Cosine correlations. However, some researchers argue that such kind of methods isolate the relations between two items without leveraging global information. The other approach learns via regression models. @cite_12 @cite_13 introduce a way to learn similarity by minimizing mean squared error between observed ratings and their corresponding estimation. @cite_18 factors similarity matrix via low-rank approximations. @cite_8 presents a weighted error function which gives more weight to the users who rated items most similar to the estimated item. @cite_3 @cite_15 simplify standard neighborhood-based models to a simple linear regression problem for top- @math recommendation based on binary databases.