We propose a new approach for Collaborative Filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (Movielens dataset) we compare the approach with the SVD- and NMF-based algorithms in terms of Mean Average Error (MAE). One of the experimental consequences is that it is enough to have a binary-scaled rating data to obtain almost the same quality in terms of MAE by BMF than for the SVD-based algorithm in case of non-scaled data.

One-class collaborative filtering or collaborative ranking with implicit feedback has been steadily receiving more attention, mostly due to the "one-class" characteristics of data in various services, e.g., "like" in Facebook and "bought" in Amazon. Previous works for solving this problem include pointwise regression methods based on absolute rating assumptions and pairwise ranking methods with relative score assumptions, where the latter was empirically found performing much better because it models users' ranking-related preferences more directly. However, the two fundamental assumptions made in the pairwise ranking methods, (1) individual pairwise preference over two items and (2) independence between two users, may not always hold. As a response, we propose a new and improved assumption, group Bayesian personalized ranking (GBPR), via introducing richer interactions among users. In particular, we introduce group preference, to relax the aforementioned individual and independence assumptions. We then design a novel algorithm correspondingly, which can recommend items more accurately as shown by various ranking-oriented evaluation metrics on four real-world datasets in our experiments.

Online rating systems are now ubiquitous due to the success of recommender systems. In such systems, users are allowed to rate the items (movies, songs, commodities) in a predefined range of values. The ratings collected can be used to infer users' preferences as well as items' intrinsic features, which are then matched to perform personalized recommendation. Most previous work focuses on improving the prediction accuracy or ranking capability. Little attention has been paid to the problem of spammers or low-reputed users in such systems. Spammers contaminate the rating system by assigning unreasonable scores to items, which may affect the accuracy of a recommender system. There are evidences supporting the existence of spammers in online rating systems. Reputation estimation methods can be employed to keep track of users' reputation and detect spammers in such systems. In this paper, we propose a unified framework for computing the reputation score of a user, given only users' ratings on items. We show that previously proposed reputation estimation methods can be captured as special cases of our framework. We propose a new low-rank matrix factorization based reputation estimation method and demonstrate its superior discrimination ability.

Trust prediction, which explores the unobserved relationships between online community users, is an emerging and important research topic in social network analysis and many web applications. Similar to other social-based recommender systems, trust relationships between users can be also modeled in the form of matrices. Recent study shows users generally establish friendship due to a few latent factors, it is therefore reasonable to assume the trust matrices are of low-rank. As a result, many recommendation system strategies can be applied here. In particular, trace norm minimization, which uses matrix's trace norm to approximate its rank, is especially appealing. However, recent articles cast doubts on the validity of trace norm approximation. In this paper, instead of using trace norm minimization, we propose a new robust rank-k matrix completion method, which explicitly seeks a matrix with exact rank. Moreover, our method is robust to noise or corrupted observations. We optimize the new objective function in an alternative manner, based on a combination of ancillary variables and Augmented Lagrangian Multiplier (ALM) Method. We perform the experiments on three real-world data sets and all empirical results demonstrate the effectiveness of our method.

Eliciting user preferences constitutes a major step towards developing recommender systems and decision support tools. Assuming that preferences are ceteris paribus allows for their concise representation as Conditional Preference Networks (CP-nets). This work presents the first empirical investigation of an algorithm for reliably and efficiently learning CP-nets in a manner that is minimally intrusive . At the same time, it introduces a novel process for efficiently reasoning with (the learned) preferences.

Matrix factorization (MF) is a popular collaborative filtering approach for recommender systems due to its simplicity and effectiveness. Existing MF methods either assume that all latent features are uncorrelated or assume that all are correlated. To address the important issue of what structure should be imposed on the features, we investigate the covariance matrix of the latent features learned from real data. Based on the findings, we propose an MF model with a sparse covariance prior which favors a sparse yet non-diagonal covariance matrix. Not only can this reflect the semantics more faithfully, but imposing sparsity can also have a side effect of preventing overfitting. Starting from a probabilistic generative model with a sparse covariance prior, we formulate the model inference problem as a maximum a posteriori (MAP) estimation problem. The optimization procedure makes use of stochastic gradient descent and majorization-minimization. For empirical validation, we conduct experiments using the MovieLens and Netflix datasets to compare the proposed method with two strong baselines which use different priors. Experimental results show that our sparse covariance prior can lead to performance improvement.

Collaborative filtering is a general technique for recommender systems, aiming to provide users with personalized recommendations. However, it suffers from two severe issues known as data sparsity and cold start. In this research, we present two different solutions to ameliorate these issues. First, we propose a trust-aware recommender system to incorporate the ratings of trusted neighbors and to form a more complete rating profile for the active users. Second, we also propose a novel Bayesian similarity measure by taking into account both the direction and length of rating profiles. Both research work shows promising empirical results based on real-world data sets. Finally, we outline the future research on trust-based clustering methods to further alleviate the concerned problems.

We propose a collaborative filtering (CF) recommendation framework which is based on viewing user feedback on products as ordinal, rather than the more common numerical view. Such an ordinal view frequently provides a more natural reflection of the user intention when providing qualitative ratings, allowing users to have different internal scoring scales. Moreover, we can address scenarios where assigning numerical scores to different types of user feedback would not be easy. The framework can wrap most collaborative filtering algorithms, enabling algorithms previously designed for numerical values to handle ordinal values. We demonstrate our framework by wrapping a leading matrix factorization CF method. A cornerstone of our method is its ability to predict a full probability distribution of the expected item ratings, rather than only a single score for an item. One of the advantages this brings is a novel approach to estimating the confidence level in each individual prediction. Compared to previous approaches to confidence estimation, ours is more principled and empirically superior in its accuracy. We demonstrate the efficacy of the approach on two of the largest publicly available datasets: the Netflix data and the Yahoo! Music data.

Collaborative filtering, a widely-used user-centric recommendation technique, predicts an item’s rating by aggregating its ratings from similar users. User similarity is usually calculated by cosine similarity or Pearson correlation coefficient. However, both of them consider only the direction of rating vectors, and suffer from a range of drawbacks. To solve these issues, we propose a novel Bayesian similarity measure based on the Dirichlet distribution, taking into consideration both the direction and length of rating vectors. Further, our principled method reduces correlation due to chance. Experimental results on six real-world data sets show that our method achieves superior accuracy.

We study the problem of diverse promoting recommendation task: selecting a subset of diverse items that can better predict a given user's preference. Recommendation techniques primarily based on user or item similarity can suffer from the risk that users cannot get expected information from the over-specified recommendation lists. In this paper, we propose an entropy regularizer to capture the notion of diversity. The entropy regularizer has good properties in that it satisfies monotonicity and submodularity, such that when we combine it with a modular rating set function, we get submodular objective function, which can be maximized approximately by efficient greedy algorithm, with provable constant factor guarantee of optimality. We apply our approach on the top-$K$ prediction problem and evaluate its performance on MovieLens data set, which is a standard database containing movie rating data collected from a popular online movie recommender system. We compare our model with the state-of-the-art recommendation algorithms. Our experiments show that the entropy regularizer effectively captures diversity and hence improves the performance of recommendation task.