Recommender systems are widely used to predict personalized preferences of goods or services using users' past activities, such as item ratings or purchase histories. If collections of such personal activities were made publicly available, they could be used to personalize a diverse range of services, including targeted advertisement or recommendations. However, there would be an accompanying risk of privacy violations. The pioneering work of Narayanan et al.\ demonstrated that even if the identifiers are eliminated, the public release of user ratings can allow for the identification of users by those who have only a small amount of data on the users' past ratings.
In this paper, we assume the following setting. A collector collects user ratings, then anonymizes and distributes them. A recommender constructs a recommender system based on the anonymized ratings provided by the collector. Based on this setting, we exhaustively list the models of recommender systems that use anonymized ratings. For each model, we then present an item-based collaborative filtering algorithm for making recommendations based on anonymized ratings. Our experimental results show that an item-based collaborative filtering based on anonymized ratings can perform better than collaborative filterings based on 5--10 non-anonymized ratings. This surprising result indicates that, in some settings, privacy protection does not necessarily reduce the usefulness of recommendations. From the experimental analysis of this counterintuitive result, we observed that the sparsity of the ratings can be reduced by anonymization and the variance of the prediction can be reduced if $k$, the anonymization parameter, is appropriately tuned. In this way, the predictive performance of recommendations based on anonymized ratings can be improved in some settings.
Matrix factorization (MF) is extensively used to mine the user preference from explicit ratings in recommender systems. However, the reliability of explicit ratings is not always consistent, because many factors may affect the user's final evaluation on an item, including commercial advertising and a friend's recommendation. Therefore, mining the reliable ratings of user is critical to further improve the performance of the recommender system. In this work, we analyze the deviation degree of each rating in overall rating distribution of user and item, and propose the notion of user-based ratin…
Multi-criteria recommender systems have been increasingly valuable for helping consumers identify the most relevant items based on different dimensions of user experiences. However, previously proposed multi-criteria models did not take into account latent embeddings generated from user reviews, which capture latent semantic relations between users and items. To address these concerns, we utilize variational autoencoders to map user reviews into latent embeddings, which are subsequently compressed into low-dimensional discrete vectors. The resulting compressed vectors constitute latent multi-c…
Fairness in recommender systems has recently received attention from researchers. Unfair recommendations have negative impact on the effectiveness of recommender systems as it may degrade users' satisfaction, loyalty, and at worst, it can lead to or perpetuate undesirable social dynamics. One of the factors that may impact fairness is calibration, the degree to which users' preferences on various item categories are reflected in the recommendations they receive. The ability of a recommendation algorithm for generating effective recommendations may depend on the meaningfulness of the input data…
Cross-domain recommendation has long been one of the major topics in recommender systems. Recently, various deep models have been proposed to transfer the learned knowledge across domains, but most of them focus on extracting abstract transferable features from auxilliary contents, e.g., images and review texts, and the patterns in the rating matrix itself is rarely touched. In this work, inspired by the concept of domain adaptation, we proposed a deep domain adaptation model (DARec) that is capable of extracting and transferring patterns from rating matrices {\em only} without relying on any …
Recommender algorithms performance is often associated with the availability of sufficient historical rating data. Unfortunately, when it comes to children, this data is seldom available. In this paper, we report on an initial analysis conducted to examine the degree to which data about traditional users, i.e., adults, can be leveraged to enhance the recommendation process for children.
How can we leverage social network data and observed ratings to correctly recommend proper items and provide a persuasive explanation for the recommendations? Many online services provide social networks among users, and it is crucial to utilize social information since recommendation by a friend is more likely to grab attention than the one from a random user. Also, explaining why items are recommended is very important in encouraging the users' actions such as actual purchases. Exploiting both ratings and social graph for recommendation, however, is not trivial because of the heterogeneity o…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Institute of Numerical Mathematics of the Russian Academy of Sciences（俄罗斯科学院数值数学研究所）
Conventional collaborative filtering techniques treat a top-n recommendations problem as a task of generating a list of the most relevant items. This formulation, however, disregards an opposite - avoiding recommendations with completely irrelevant items. Due to that bias, standard algorithms, as well as commonly used evaluation metrics, become insensitive to negative feedback. In order to resolve this problem we propose to treat user feedback as a categorical variable and model it with users and items in a ternary way. We employ a third-order tensor factorization technique and implement a hig…
Beijing University of Posts and Telecommunications（北京邮电大学）
Cross-domain recommendation has been proposed to transfer user behavior pattern by pooling together the rating data from multiple domains to alleviate the sparsity problem appearing in single rating domains. However, previous models only assume that multiple domains share a latent common rating pattern based on the user-item co-clustering. To capture diversities among different domains, we propose a novel Probabilistic Cluster-level Latent Factor (PCLF) model to improve the cross-domain recommendation performance. Experiments on several real world datasets demonstrate that our proposed model o…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）
Exploiting low-rank structure of the user-item rating matrix has been the crux of many recommendation engines. However, existing recommendation engines force raters with heterogeneous behavior profiles to map their intrinsic rating scales to a common rating scale (e.g. 1-5). This non-linear transformation of the rating scale shatters the low-rank structure of the rating matrix, therefore resulting in a poor fit and consequentially, poor recommendations. In this paper, we propose Clustered Monotone Transforms for Rating Factorization (CMTRF), a novel approach to perform regression up to unknown…
Knowledge Graphs (KGs) have been integrated in several models of recommendation to augment the informational value of an item by means of its related entities in the graph. Yet, existing datasets only provide explicit ratings on items and no information is provided about user opinions of other (non-recommendable) entities. To overcome this limitation, we introduce a new dataset, called the MindReader, providing explicit user ratings both for items and for KG entities. In this first version, the MindReader dataset provides more than 102 thousands explicit ratings collected from 1,174 real users…
Collaborative filtering algorithms find useful patterns in rating and consumption data and exploit these patterns to guide users to good items. Many of the patterns in rating datasets reflect important real-world differences between the various users and items in the data; other patterns may be irrelevant or possibly undesirable for social or ethical reasons, particularly if they reflect undesired discrimination, such as discrimination in publishing or purchasing against authors who are women or ethnic minorities. In this work, we examine the response of collaborative filtering recommender alg…
Rating prediction is a core problem in recommender systems to quantify user's preferences towards items, however, rating imbalance naturally roots in real-world user ratings that cause biased predictions and lead to poor performance on tail ratings. While existing approaches in the rating prediction task deploy weighted cross-entropy to re-weight training samples, such approaches commonly assume an normal distribution, a symmetrical and balanced space. In contrast to the normal assumption, we propose a novel \underline{\emph{G}}umbel-based \underline{\emph{V}}ariational \underline{\emph{N}}etw…
DePaul University（德保罗大学）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
It is well known that explicit user ratings in recommender systems are biased towards high ratings, and that users differ significantly in their usage of the rating scale. Implementers usually compensate for these issues through rating normalization or the inclusion of a user bias term in factorization models. However, these methods adjust only for the central tendency of users' distributions. In this work, we demonstrate that lack of \textit{flatness} in rating distributions is negatively correlated with recommendation performance. We propose a rating transformation model that compensates for…
As the number of Web services with the same or similar functions increases steadily on the Internet, nowadays more and more service consumers pay great attention to the non-functional properties of Web services, also known as quality of service (QoS), when finding and selecting appropriate Web services. For most of the QoS-aware Web service recommendation systems, the list of recommended Web services is generally obtained based on a rating-oriented prediction approach, aiming at predicting the potential ratings that an active user may assign to the unrated services as accurately as possible. H…
Recommender systems (RSs) have been a widely exploited approach to solving the information overload problem. However, the performance is still limited due to the extreme sparsity of the rating data. With the popularity of Web 2.0, the social tagging system provides more external information to improve recommendation accuracy. Although some existing approaches combine the matrix factorization models with co-occurrence properties and context of tags, they neglect the issue of tag sparsity without the commonly associated tags problem that would also result in inaccurate recommendations. Consequen…
Recommender systems recommend items more accurately by analyzing users' potential interest on different brands' items. In conjunction with users' rating similarity, the presence of users' implicit feedbacks like clicking items, viewing items specifications, watching videos etc. have been proved to be helpful for learning users' embedding, that helps better rating prediction of users. Most existing recommender systems focus on modeling of ratings and implicit feedbacks ignoring users' explicit feedbacks. Explicit feedbacks can be used to validate the reliability of the particular users and can …
The video game industry is larger than both the film and music industries combined. Recommender systems for video games have received relatively scant academic attention, despite the uniqueness of the medium and its data. In this paper, we introduce a graph-based recommender system that makes use of interactivity, arguably the most significant feature of video gaming. We show that the use of implicit data that tracks user-game interactions and levels of attainment (e.g. Sony Playstation Trophies, Microsoft Xbox Achievements) has high predictive value when making recommendations. Furthermore, w…
National Key Laboratory for Novel Software Technology（新型软件技术国家重点实验室）；Nanjing University（南京大学）；Hong Kong Baptist University（香港浸会大学）
Recommender systems (RSs) provide an effective way of alleviating the information overload problem by selecting personalized choices. Online social networks and user-generated content provide diverse sources for recommendation beyond ratings, which present opportunities as well as challenges for traditional RSs. Although social matrix factorization (Social MF) can integrate ratings with social relations and topic matrix factorization can integrate ratings with item reviews, both of them ignore some useful information. In this paper, we investigate the effective data fusion by combining the two…
University P. et M. Curie, Sorbonne-Universités（皮埃尔与玛丽·居里大学（索邦大学））；CNRS（法国国家科学研究中心）
We propose to augment rating based recommender systems by providing the user with additional information which might help him in his choice or in the understanding of the recommendation. We consider here as a new task, the generation of personalized reviews associated to items. We use an extractive summary formulation for generating these reviews. We also show that the two information sources, ratings and items could be used both for estimating ratings and for generating summaries, leading to improved performance for each system compared to the use of a single source. Besides these two contrib…
Collaborative Filtering is largely applied to personalize item recommendation but its performance is affected by the sparsity of rating data. In order to address this issue, recent systems have been developed to improve recommendation by extracting latent factors from the rating matrices, or by exploiting trust relations established among users in social networks. In this work, we are interested in evaluating whether other sources of preference information than ratings and social ties can be used to improve recommendation performance. Specifically, we aim at testing whether the integration of …
Universidad Autónoma de Madrid（马德里自治大学）；Pontificia Universidad Católica de Chile（智利天主教大学）
The success of neural network embeddings has entailed a renewed interest in using knowledge graphs for a wide variety of machine learning and information retrieval tasks. In particular, recent recommendation methods based on graph embeddings have shown state-of-the-art performance. In general, these methods encode latent rating patterns and content features. Differently from previous work, in this paper, we propose to exploit embeddings extracted from graphs that combine information from ratings and aspect-based opinions expressed in textual reviews. We then adapt and evaluate state-of-the-art…
Recommendation systems are an important units in today's e-commerce applications, such as targeted advertising, personalized marketing and information retrieval. In recent years, the importance of contextual information has motivated generation of personalized recommendations according to the available contextual information of users. Compared to the traditional systems which mainly utilize users' rating history, review-based recommendation hopefully provide more relevant results to users. We introduce a review-based recommendation approach that obtains contextual information by mining user re…
Recommender systems have been studied extensively due to their practical use in many real-world scenarios. Despite this, generating effective recommendations with sparse user ratings remains a challenge. Side information associated with items has been widely utilized to address rating sparsity. Existing recommendation models that use side information are linear and, hence, have restricted expressiveness. Deep learning has been used to capture non-linearities by learning deep item representations from side information but as side information is high-dimensional existing deep models tend to have…
Tsinghua University（清华大学）；Cornell University（康奈尔大学）；University of Connecticut（康涅狄格大学）；Weill Cornell Medicine（威尔康奈尔医学院）
Selection bias is prevalent in the data for training and evaluating recommendation systems with explicit feedback. For example, users tend to rate items they like. However, when rating an item concerning a specific user, most of the recommendation algorithms tend to rely too much on his/her rating (feedback) history. This introduces implicit bias on the recommendation system, which is referred to as user feedback-loop bias in this paper. We propose a systematic and dynamic way to correct such bias and to obtain more diverse and objective recommendations by utilizing temporal rating information…
The Chinese University of Hong Kong（香港中文大学）；Tencent Inc.（腾讯公司）
Recently, some E-commerce sites launch a new interaction box called Tips on their mobile apps. Users can express their experience and feelings or provide suggestions using short texts typically several words or one sentence. In essence, writing some tips and giving a numerical rating are two facets of a user's product assessment action, expressing the user experience and feelings. Jointly modeling these two facets is helpful for designing a better recommendation system. While some existing models integrate text information such as item specifications or user reviews into user and item latent f…
Collaborative filtering is a broad and powerful framework for building recommendation systems that has seen widespread adoption. Over the past decade, the propensity of such systems for favoring popular products and thus creating echo chambers have been observed. This has given rise to an active area of research that seeks to diversify recommendations generated by such algorithms. We address the problem of increasing diversity in recommendation systems that are based on collaborative filtering that use past ratings to predicting a rating quality for potential recommendations. Following our ear…
Universidad Autónoma de Madrid（马德里自治大学）；Pontificia Universidad Católica de Chile（智利天主教大学）
The success of neural network embeddings has entailed a renewed interest in using knowledge graphs for a wide variety of machine learning and information retrieval tasks. In particular, current recommendation methods based on graph embeddings have shown state-of-the-art performance. These methods commonly encode latent rating patterns and content features. Different from previous work, in this paper, we propose to exploit embeddings extracted from graphs that combine information from ratings and aspect-based opinions expressed in textual reviews. We then adapt and evaluate state-of-the-art gra…
Recommending items to users is a challenging task due to the large amount of missing information. In many cases, the data solely consist of ratings or tags voluntarily contributed by each user on a very limited subset of the available items, so that most of the data of potential interest is actually missing. Current approaches to recommendation usually assume that the unobserved data is missing at random. In this contribution, we provide statistical evidence that existing movie recommendation datasets reveal a significant positive association between the rating of items and the propensity to s…
Accurate recommendation and reliable explanation are two key issues for modern recommender systems. However, most recommendation benchmarks only concern the prediction of user-item ratings while omitting the underlying causes behind the ratings. For example, the widely-used Yahoo!R3 dataset contains little information on the causes of the user-movie ratings. A solution could be to conduct surveys and require the users to provide such information. In practice, the user surveys can hardly avoid compliance issues and sparse user responses, which greatly hinders the exploration of causality-based …
In recent years, Variational Autoencoders (VAEs) have been shown to be highly effective in both standard collaborative filtering applications and extensions such as incorporation of implicit feedback. We extend VAEs to collaborative filtering with side information, for instance when ratings are combined with explicit text feedback from the user. Instead of using a user-agnostic standard Gaussian prior, we incorporate user-dependent priors in the latent VAE space to encode users' preferences as functions of the review text. Taking into account both the rating and the text information to represe…
With over 500 million tweets posted per day, in Twitter, it is difficult for Twitter users to discover interesting content from the deluge of uninteresting posts. In this work, we present a novel, explainable, topical recommendation system, that utilizes social annotations, to help Twitter users discover tweets, on topics of their interest. A major challenge in using traditional rating dependent recommendation systems, like collaborative filtering and content based systems, in high volume social networks is that, due to attention scarcity most items do not get any ratings. Additionally, the fa…
Although latent factor models (e.g., matrix factorization) achieve good accuracy in rating prediction, they suffer from several problems including cold-start, non-transparency, and suboptimal recommendation for local users or items. In this paper, we employ textual review information with ratings to tackle these limitations. Firstly, we apply a proposed aspect-aware topic model (ATM) on the review text to model user preferences and item features from different aspects, and estimate the aspect importance of a user towards an item. The aspect importance is then integrated into a novel aspect-awa…
Reviews contain rich information about product characteristics and user interests and thus are commonly used to boost recommender system performance. Specifically, previous work show that jointly learning to perform review generation improves rating prediction performance. Meanwhile, these model-produced reviews serve as recommendation explanations, providing the user with insights on predicted ratings. However, while existing models could generate fluent, human-like reviews, it is unclear to what degree the reviews fully uncover the rationale behind the jointly predicted rating. In this work,…
Collaborative filtering problems are commonly solved based on matrix completion techniques which recover the missing values of user-item interaction matrices. In a matrix, the rating position specifically represents the user given and the item rated. Previous matrix completion techniques tend to neglect the position of each element (user, item and ratings) in the matrix but mainly focus on semantic similarity between users and items to predict the missing value in a matrix. This paper proposes a novel position-enhanced user/item representation training model for recommendation, SUPER-Rec. We f…
Free University of Bozen-Bolzano（博尔扎诺自由大学）；Roma Tre University（罗马第三大学）
Finding online research papers relevant to one's interests is very challenging due to the increasing number of publications. Therefore, personalized research paper recommendation has become a significant and timely research topic. Collaborative filtering is a successful recommendation approach, which exploits the ratings given to items by users as a source of information for learning to make accurate recommendations. However, the ratings are often very sparse as in the research paper domain, due to the huge number of publications growing every year. Therefore, more attention has been drawn to …
Although the latent factor model achieves good accuracy in rating prediction, it suffers from many problems including cold-start, non-transparency, and suboptimal results for individual user-item pairs. In this paper, we exploit textual reviews and item images together with ratings to tackle these limitations. Specifically, we first apply a proposed multi-modal aspect-aware topic model (MATM) on text reviews and item images to model users' preferences and items' features from different aspects, and also estimate the aspect importance of a user towards an item. Then the aspect importance is int…
Recently, user-oriented auto-encoders (UAEs) have been widely used in recommender systems to learn semantic representations of users based on their historical ratings. However, since latent item variables are not modeled in UAE, it is difficult to utilize the widely available item content information when ratings are sparse. In addition, whenever new items arrive, we need to wait for collecting rating data for these items and retrain the UAE from scratch, which is inefficient in practice. Aiming to address the above two problems simultaneously, we propose a mutually-regularized dual collaborat…
Recommendation system has been widely used in different areas. Collaborative filtering focuses on rating, ignoring the features of items itself. In order to effectively evaluate customers preferences on books, taking into consideration of the characteristics of offline book retail, we use LDA model to calculate customers preference on book topics and use word2vec to calculate customers preference on book types. When forecasting rating on books, we take two factors into consideration: similarity of customers and correlation between customers and books. The experiment shows that our hybrid recom…
Consensus-Driven Group Recommendation on Sparse Explicit Feedback: A Collaborative Filtering and Choquet-Borda Aggregation Framework
Hanoi University of Business and Technology（河内工商大学）；Intracom University, Vietnam（越南 Intracom 大学）；Pitech lab, Hanoi, Vietnam（河内 Pitech 实验室）；Appen Data Technology, Vietnam（越南 Appen 数据技术公司）；Hai Phong University, Vietnam（越南海防大学）
Currently, there starts a research trend to leverage neural architecture for recommendation systems. Though several deep recommender models are proposed, most methods are too simple to characterize users' complex preference. In this paper, for a fine-grain analysis, users' ratings are explained from multiple perspectives, based on which, we propose our neural architecture. Specifically, our model employs several sequential stages to encode the user and item into hidden representations. In one stage, the user and item are represented from multiple perspectives and in each perspective, the repre…
Pairwise and Attribute-Aware Decision Tree-Based Preference Elicitation for Cold-Start Recommendation
KU Leuven, Campus Kulak, Department of Public Health and Primary Care（KU莱顿大学）；Itec, imec research group at KU Leuven（Itec）；KU Leuven, Department of Mathematics（KU莱顿大学）
In the last decade, driven also by the availability of an unprecedented computational power and storage capabilities in cloud environments we assisted to the proliferation of new algorithms, methods, and approaches in two areas of artificial intelligence: knowledge representation and machine learning. On the one side, the generation of a high rate of structured data on the Web led to the creation and publication of the so-called knowledge graphs. On the other side, deep learning emerged as one of the most promising approaches in the generation and training of models that can be applied to a wi…
Traditional Recommender Systems (RS) do not consider any personal user information beyond rating history. Such information, on the other hand, is widely available on social networking sites (Facebook, Twitter). As a result, social networks have recently been used in recommendation systems. In this paper, we propose an efficient method for incorporating social signals into the recommendation process by building a trust network which supplements the users' rating profiles. We first show the effect of different cold-start users types on the Collaborative Filtering (CF) technique in several real-w…
Modern E-commerce websites contain heterogeneous sources of information, such as numerical ratings, textual reviews and images. These information can be utilized to assist recommendation. Through textual reviews, a user explicitly express her affinity towards the item. Previous researchers found that by using the information extracted from these reviews, we can better profile the users' explicit preferences as well as the item features, leading to the improvement of recommendation performance. However, most of the previous algorithms were only utilizing the review information for explicit-feed…
Understanding user preference is essential to the optimization of recommender systems. As a feedback of user's taste, rating scores can directly reflect the preference of a given user to a given product. Uncovering the latent components of user ratings is thus of significant importance for learning user interests. In this paper, a new recommendation approach, called LCR, was proposed by investigating the latent components of user ratings. The basic idea is to decompose an existing rating into several components via a cost-sensitive learning strategy. Specifically, each rating is assigned to se…
This paper proposes a number of explicit and implicit ratings in product recommendation system for Business-to-customer e-commerce purposes. The system recommends the products to a new user. It depends on the purchase pattern of previous users whose purchase pattern is close to that of a user who asks for a recommendation. The system is based on weighted cosine similarity measure to find out the closest user profile among the profiles of all users in database. It also implements Association rule mining rule in recommending the products. Also, this product recommendation system takes into consi…
Both reviews and user-item interactions (i.e., rating scores) have been widely adopted for user rating prediction. However, these existing techniques mainly extract the latent representations for users and items in an independent and static manner. That is, a single static feature vector is derived to encode her preference without considering the particular characteristics of each candidate item. We argue that this static encoding scheme is difficult to fully capture the users' preference. In this paper, we propose a novel context-aware user-item representation learning model for rating predic…
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）
Cross-Domain Recommendation (CDR) has been popularly studied to utilize different domain knowledge to solve the data sparsity and cold-start problem in recommender systems. In this paper, we focus on the Review-based Non-overlapped Recommendation (RNCDR) problem. The problem is commonly-existed and challenging due to two main aspects, i.e, there are only positive user-item ratings on the target domain and there is no overlapped user across different domains. Most previous CDR approaches cannot solve the RNCDR problem well, since (1) they cannot effectively combine review with other information…
Sorbonne Universités, UPMC Univ Paris 06（索邦大学，巴黎第六大学（UPMC））；Ecole Centrale Marseille（马赛中央理工学院）；Aix-Marseille Univ.（艾克斯-马赛大学）
A standard approach to Collaborative Filtering (CF), i.e. prediction of user ratings on items, relies on Matrix Factorization techniques. Representations for both users and items are computed from the observed ratings and used for prediction. Unfortunatly, these transductive approaches cannot handle the case of new users arriving in the system, with no known rating, a problem known as user cold-start. A common approach in this context is to ask these incoming users for a few initialization ratings. This paper presents a model to tackle this twofold problem of (i) finding good questions to ask,…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Carnegie Mellon University（卡内基梅隆大学）
Current recommender systems exploit user and item similarities by collaborative filtering. Some advanced methods also consider the temporal evolution of item ratings as a global background process. However, all prior methods disregard the individual evolution of a user's experience level and how this is expressed in the user's writing in a review community. In this paper, we model the joint evolution of user experience, interest in specific item facets, writing style, and rating behavior. This way we can generate individual recommendations that take into account the user's maturity level (e.g.…
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；School of Information Science and Engineering, University of Chinese Academy of Sciences（中国科学院大学信息科学与工程学院）
Restricted Boltzman Machines (RBMs) have been successfully used in recommender systems. However, as with most of other collaborative filtering techniques, it cannot solve cold start problems for there is no rating for a new item. In this paper, we first apply conditional RBM (CRBM) which could take extra information into account and show that CRBM could solve cold start problem very well, especially for rating prediction task. CRBM naturally combine the content and collaborative data under a single framework which could be fitted effectively. Experiments show that CRBM can be compared favourab…
King Saud University（沙特国王大学）；College of Computer and Information Sciences（计算机与信息科学学院）
Recommender systems have become an essential tool for providers and users of online services and goods, especially with the increased use of the Internet to access information and purchase products and services. This work proposes a novel recommendation method based on complex networks generated by a similarity-popularity model to predict ones. We first construct a model of a network having users and items as nodes from observed ratings and then use it to predict unseen ratings. The prospect of producing accurate rating predictions using a similarity-popularity model with hidden metric spaces …
