Attribute-Aware Recommender System Based on Collaborative Filtering: Survey and Classification <s> Collaborative Filtering and Matrix Factorization <s> This paper presents an overview of the field of recommender systems and describes the current generation of recommendation methods that are usually classified into the following three main categories: content-based, collaborative, and hybrid recommendation approaches. This paper also describes various limitations of current recommendation methods and discusses possible extensions that can improve recommendation capabilities and make recommender systems applicable to an even broader range of applications. These extensions include, among others, an improvement of understanding of users and items, incorporation of the contextual information into the recommendation process, support for multicriteria ratings, and a provision of more flexible and less intrusive types of recommendations. <s> BIB001 </s> Attribute-Aware Recommender System Based on Collaborative Filtering: Survey and Classification <s> Collaborative Filtering and Matrix Factorization <s> 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. <s> BIB002 </s> Attribute-Aware Recommender System Based on Collaborative Filtering: Survey and Classification <s> Collaborative Filtering and Matrix Factorization <s> Over the past two decades, a large amount of research effort has been devoted to developing algorithms that generate recommendations. The resulting research progress has established the importance of the user-item (U-I) matrix, which encodes the individual preferences of users for items in a collection, for recommender systems. The U-I matrix provides the basis for collaborative filtering (CF) techniques, the dominant framework for recommender systems. Currently, new recommendation scenarios are emerging that offer promising new information that goes beyond the U-I matrix. This information can be divided into two categories related to its source: rich side information concerning users and items, and interaction information associated with the interplay of users and items. In this survey, we summarize and analyze recommendation scenarios involving information sources and the CF algorithms that have been recently developed to address them. We provide a comprehensive introduction to a large body of research, more than 200 key references, with the aim of supporting the further development of recommender systems exploiting information beyond the U-I matrix. On the basis of this material, we identify and discuss what we see as the central challenges lying ahead for recommender system technology, both in terms of extensions of existing techniques as well as of the integration of techniques and technologies drawn from other research areas. <s> BIB003 </s> Attribute-Aware Recommender System Based on Collaborative Filtering: Survey and Classification <s> Collaborative Filtering and Matrix Factorization <s> Abstract On the Internet, where the number of choices is overwhelming, there is need to filter, prioritize and efficiently deliver relevant information in order to alleviate the problem of information overload, which has created a potential problem to many Internet users. Recommender systems solve this problem by searching through large volume of dynamically generated information to provide users with personalized content and services. This paper explores the different characteristics and potentials of different prediction techniques in recommendation systems in order to serve as a compass for research and practice in the field of recommendation systems. <s> BIB004 </s> Attribute-Aware Recommender System Based on Collaborative Filtering: Survey and Classification <s> Collaborative Filtering and Matrix Factorization <s> The collaborative filtering (CF) approach to recommenders has recently enjoyed much interest and progress. The fact that it played a central role within the recently completed Netflix competition has contributed to its popularity. This chapter surveys the recent progress in the field. Matrix factorization techniques, which became a first choice for implementing CF, are described together with recent innovations. We also describe several extensions that bring competitive accuracy into neighborhood methods, which used to dominate the field. The chapter demonstrates how to utilize temporal models and implicit feedback to extend models accuracy. In passing, we include detailed descriptions of some the central methods developed for tackling the challenge of the Netflix Prize competition. <s> BIB005
Collaborative filtering (CF) has become the prevailing technique for realizing recommender systems in recent years Tuzhilin, 2005, 2011; BIB003 BIB004 . It assumes that the preferences users exhibit for items they have interacted with can be generalized and used to infer their preferences regarding items they have never interacted with by leveraging the records of other users with similar preferences. This section briefly introduces conventional CF techniques, which assume the availability of only user-item interactions or the rating matrix R. In practice, they are commonly categorized into memory-based CF and model-based CF BIB001 BIB003 BIB004 . Memory-based CF directly exploits rows or columns in the rating matrix R as representations of users or items and identifies a group of similar users or items using a pre-defined similarity measure. Commonly used similarity metrics include the Pearson correlation, the Jaccard similarity coefficient, the cosine similarity, or their variants. Memory-based CF techniques can be divided into user-based and item-based approaches, which identify either a group of similar users or similar items, respectively. For user-based approaches, K nearest neighborsor the K most similar users-are extracted, and their preferences or ratings regarding a target item are aggregated into a rating prediction using similarities between users as weights. The rating prediction for user u on item i,r ui , can be formulated as: where function sim(·) is a similarity measure, Z is the normalization constant, and U u is the set of similar users to user u BIB003 . Rating predictions of item-based approaches can be formulated in a similar way. The calculated pairwise similarities between users or items act as the memory of the recommender system since they can be saved for generating later recommendations. Model-based CF, on the other hand, takes the rating matrix R to train a predictive model with a set of parameters θ to make recommendations BIB001 BIB003 . Predictive models can be formulated as a function that outputs ratings for rating predictions or numerical preference scores for item ranking given a user-item pair (u, i): Model-based CF then ranks and selects the K items with the highest ratings or scores r ui as recommendations. Common core algorithms for model-based CF involve Bayesian classifiers, clustering techniques, graph-based approaches, genetic algorithms, and dimension-reduction methods such as Singular Value Decomposition (SVD) Tuzhilin, 2005, 2011; Bobadilla et al., 2013; BIB003 BIB004 . Over the last decade, a class of latent factor models, called matrix factorization, has been popularized and is commonly adopted as the basis of advanced techniques because of its success in the development of algorithms for the Netflix competition BIB002 BIB005 . In general, latent factor models aim to learn a low-dimensional representation, or latent factor, for each entity and combine the latent factors of different entities using specific methods such as inner product, bilinear map, or neural networks to make predictions. As one of these latent factor models, matrix factorization for recommender systems characterizes each user and item by a low-dimensional vector and predicts ratings based on inner product. Matrix factorization (MF)  BIB002 BIB005 BIB003 , in the basic form, represents each user u as a parameter vector w u ∈ R K and each item i as h i ∈ R K , where K is the dimension of latent factors. The prediction of user u's rating or preference regarding item i, denoted asr ui , can be computed using the inner product: which captures the interaction between them. MF seeks to generate rating predictions that are as close as possible to those recorded ratings. In matrix form, it can be written as finding MF is essentially learning a low-rank approximation of the rating matrix, since the dimension of representations K is usually much smaller than the number of users N u and items N i . To learn the latent factors of users and items, the system tries to find W, H that minimizes the regularized square error on the set of entries of known ratings in R [denoted as δ(R)]: where λ W and λ H are regularization parameters. MF tends to cluster users or items with similar rating configurations into groups in the latent factor space, which implies that similar users or items will be close to each other. Furthermore, MF assumes that the rank of rating matrix R or the dimension of the vector space generated by the rating configuration of users is far smaller than the number of users N u . This implies that each user's rating configuration can be obtained by a linear combination of ratings from a group of other users since they are all generated by K principal vectors. Thus, MF is in the spirit of collaborative filtering, which is to infer a user's unknown ratings by the ratings of several other users. Biased matrix factorization  BIB002 BIB005 , an improvement of MF, models the characteristics of each user and each item and the global tendency that are independent of user-item interactions. The obvious drawback of MF is that only user-item interactions w ⊤ u h i are considered in rating predictions. However, ratings usually contain universal shifts or exhibit systematic tendencies with respect to users and items. For instance, there might be a group of users inclined to give significantly higher ratings than others or a group of items widely considered to be of high-quality and that receive higher ratings. Besides, it is common that all ratings are non-negative, which implies that the overall average might not be close to zero and causes a difficulty for training small-valueinitialized representations. Due to the issues mentioned above, biased MF augments MF rating predictions with linear biases that account for user-related, item-related, and global effects. The rating prediction is extended as follows: where µ, c i , d j are global bias, bias of user i, and bias of item j, respectively. Biased MF then finds the optimal W, H, c, d, µ that minimizes the regularized square error as follows: where W 2 F = N u u=1 w u 2 2 denotes the squared Frobenius norm. The regularization parameter λ is tuned by cross-validation. Probabilistic matrix factorization (PMF, Figure 2 and Biased PMF, Figure 3 ) Mnih, 2007, 2008) is a probabilistic linear model with observed Gaussian noise and can be viewed as a probabilistic extension of MF. PMF adopts the assumption that users and items are independent and represents each user or each item with a zero-mean spherical multivariate Gaussian distribution as follows: where σ 2 W and σ 2 H are observed user-specific and item-specific noise. PMF then formulates the conditional probability over the observed ratings as where δ(R) is the set of known ratings and N (x | µ, σ 2 ) denotes the Gaussian distribution with mean µ and variance σ 2 . Learning in PMF is conducted by maximum a posteriori (MAP) estimation, which is equivalent to maximizing the log of the posterior distribution of W, H: where C is a constant independent of all parameters and K is the dimension of user or item representations. With Gaussian noise σ 2 R , σ 2 W , σ 2 H observed, maximizing the log-posterior is identical to minimizing the objective function with the form: Frontiers in Big Data | www.frontiersin.org FIGURE 4 | Model design flow of an attribute-aware collaborative filtering-based recommender system. When reading ratings and attributes for a proposed approach, we have to consider the sources and the types of attributes or ratings, which could affect the recommendation goals and model designs. The evaluation of a proposed recommender system depends heavily on the chosen recommendation goals. where Note that (10) has exactly the same form as the regularized square error of MF, and gradient descent or its extensions can then be applied in training PMF. Since collaborative filtering techniques only consider rating matrix R in making recommendations, they cannot discover the preferences of users or for items with scant user-item interactions. This problem is referred as the cold-start issue. In section 3, we will review recommendation systems that extend CF to incorporate contexts or rich side information regarding users and items to alleviate the cold-start problem.