This paper proposes Quaternion Collaborative Filtering (QCF), a novel representation learning method for recommendation. Our proposed QCF relies on and exploits computation with Quaternion algebra, benefiting from the expressiveness and rich representation learning capability of Hamilton products. Quaternion representations, based on hypercomplex numbers, enable rich inter-latent dependencies between imaginary components. This encourages intricate relations to be captured when learning user-item interactions, serving as a strong inductive bias as compared with the real-space inner product. All in all, we conduct extensive experiments on six real-world datasets, demonstrating the effectiveness of Quaternion algebra in recommender systems. The results exhibit that QCF outperforms a wide spectrum of strong neural baselines on all datasets. Ablative experiments confirm the effectiveness of Hamilton-based composition over multi-embedding composition in real space.
With the growing volume of online information, recommender systems have been an effective strategy to overcome information overload. The utility of recommender systems cannot be overstated, given their widespread adoption in many web applications, along with their potential impact to ameliorate many problems related to over-choice. In recent years, deep learning has garnered considerable interest in many research fields such as computer vision and natural language processing, owing not only to stellar performance but also to the attractive property of learning feature representations from scratch. The influence of deep learning is also pervasive, recently demonstrating its effectiveness when applied to information retrieval and recommender systems research. The field of deep learning in recommender system is flourishing. This article aims to provide a comprehensive review of recent research efforts on deep learning-based recommender systems. More concretely, we provide and devise a taxonomy of deep learning-based recommendation models, along with a comprehensive summary of the state of the art. Finally, we expand on current trends and provide new perspectives pertaining to this new and exciting development of the field. This paper proposes AutoRec, a novel autoencoder framework for collaborative filtering (CF). Empirically, AutoRec's compact and efficiently trainable model outperforms state-of-the-art CF techniques (biased matrix factorization, RBM-CF and LLORMA) on the Movielens and Netflix datasets. We apply recurrent neural networks (RNN) on a new domain, namely recommender systems. Real-life recommender systems often face the problem of having to base recommendations only on short session-based data (e.g. a small sportsware website) instead of long user histories (as in the case of Netflix). In this situation the frequently praised matrix factorization approaches are not accurate. This problem is usually overcome in practice by resorting to item-to-item recommendations, i.e. recommending similar items. We argue that by modeling the whole session, more accurate recommendations can be provided. We therefore propose an RNN-based approach for session-based recommendations. Our approach also considers practical aspects of the task and introduces several modifications to classic RNNs such as a ranking loss function that make it more viable for this specific problem. Experimental results on two data-sets show marked improvements over widely used approaches. Recommender systems traditionally assume that user profiles and movie attributes are static. Temporal dynamics are purely reactive, that is, they are inferred after they are observed, e.g. after a user's taste has changed or based on hand-engineered temporal bias corrections for movies. We propose Recurrent Recommender Networks (RRN) that are able to predict future behavioral trajectories. This is achieved by endowing both users and movies with a Long Short-Term Memory (LSTM) autoregressive model that captures dynamics, in addition to a more traditional low-rank factorization. On multiple real-world datasets, our model offers excellent prediction accuracy and it is very compact, since we need not learn latent state but rather just the state transition function. Modeling user-item interaction patterns is an important task for personalized recommendations. Many recommender systems are based on the assumption that there exists a linear relationship between users and items while neglecting the intricacy and non-linearity of real-life historical interactions. In this paper, we propose a neural network based recommendation model (NeuRec) that untangles the complexity of user-item interactions and establishes an integrated network to combine non-linear transformation with latent factors. We further design two variants of NeuRec: user-based NeuRec and item-based NeuRec, by concentrating on different aspects of the interaction matrix. Extensive experiments on four real-world datasets demonstrated their superior performances on personalized ranking task. Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix factorization approximates the entries of the matrix by a simple, fixed function---namely, the inner product---acting on the latent feature vectors for the corresponding row and column. Here we consider replacing the inner product by an arbitrary function that we learn from the data at the same time as we learn the latent feature vectors. In particular, we replace the inner product by a multi-layer feed-forward neural network, and learn by alternating between optimizing the network for fixed latent features, and optimizing the latent features for a fixed network. The resulting approach---which we call neural network matrix factorization or NNMF, for short---dominates standard low-rank techniques on a suite of benchmark but is dominated by some recent proposals that take advantage of the graph features. Given the vast range of architectures, activation functions, regularizers, and optimization techniques that could be used within the NNMF framework, it seems likely the true potential of the approach has yet to be reached. This paper contributes improvements on both the effectiveness and efficiency of Matrix Factorization (MF) methods for implicit feedback. We highlight two critical issues of existing works. First, due to the large space of unobserved feedback, most existing works resort to assign a uniform weight to the missing data to reduce computational complexity. However, such a uniform assumption is invalid in real-world settings. Second, most methods are also designed in an offline setting and fail to keep up with the dynamic nature of online data. We address the above two issues in learning MF models from implicit feedback. We first propose to weight the missing data based on item popularity, which is more effective and flexible than the uniform-weight assumption. However, such a non-uniform weighting poses efficiency challenge in learning the model. To address this, we specifically design a new learning algorithm based on the element-wise Alternating Least Squares (eALS) technique, for efficiently optimizing a MF model with variably-weighted missing data. We exploit this efficiency to then seamlessly devise an incremental update strategy that instantly refreshes a MF model given new feedback. Through comprehensive experiments on two public datasets in both offline and online protocols, we show that our implemented, open-source (https: github.com hexiangnan sigir16-eals) eALS consistently outperforms state-of-the-art implicit MF methods.    Automatic music recommendation has become an increasingly relevant problem in recent years, since a lot of music is now sold and consumed digitally. Most recommender systems rely on collaborative filtering. However, this approach suffers from the cold start problem: it fails when no usage data is available, so it is not effective for recommending new and unpopular songs. In this paper, we propose to use a latent factor model for recommendation, and predict the latent factors from music audio when they cannot be obtained from usage data. We compare a traditional approach using a bag-of-words representation of the audio signals with deep convolutional neural networks, and evaluate the predictions quantitatively and qualitatively on the Million Song Dataset. We show that using predicted latent factors produces sensible recommendations, despite the fact that there is a large semantic gap between the characteristics of a song that affect user preference and the corresponding audio signal. We also show that recent advances in deep learning translate very well to the music recommendation setting, with deep convolutional neural networks significantly outperforming the traditional approach. 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. In recent years, deep neural networks have yielded immense success on speech recognition, computer vision and natural language processing. However, the exploration of deep neural networks on recommender systems has received relatively less scrutiny. In this work, we strive to develop techniques based on neural networks to tackle the key problem in recommendation --- collaborative filtering --- on the basis of implicit feedback. Although some recent work has employed deep learning for recommendation, they primarily used it to model auxiliary information, such as textual descriptions of items and acoustic features of musics. When it comes to model the key factor in collaborative filtering --- the interaction between user and item features, they still resorted to matrix factorization and applied an inner product on the latent features of users and items. By replacing the inner product with a neural architecture that can learn an arbitrary function from data, we present a general framework named NCF, short for Neural network-based Collaborative Filtering. NCF is generic and can express and generalize matrix factorization under its framework. To supercharge NCF modelling with non-linearities, we propose to leverage a multi-layer perceptron to learn the user-item interaction function. Extensive experiments on two real-world datasets show significant improvements of our proposed NCF framework over the state-of-the-art methods. Empirical evidence shows that using deeper layers of neural networks offers better recommendation performance. Collaborative filtering (CF) has been successfully used to provide users with personalized products and services. However, dealing with the increasing sparseness of user-item matrix still remains a challenge. To tackle such issue, hybrid CF such as combining with content based filtering and leveraging side information of users and items has been extensively studied to enhance performance. However, most of these approaches depend on hand-crafted feature engineering, which is usually noise-prone and biased by different feature extraction and selection schemes. In this paper, we propose a new hybrid model by generalizing contractive auto-encoder paradigm into matrix factorization framework with good scalability and computational efficiency, which jointly models content information as representations of effectiveness and compactness, and leverage implicit user feedback to make accurate recommendations. Extensive experiments conducted over three large-scale real datasets indicate the proposed approach outperforms the compared methods for item recommendation. 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 k-nearest-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. 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. Deep learning based recommender systems have been extensively explored in recent years. However, the large number of models proposed each year poses a big challenge for both researchers and practitioners in reproducing the results for further comparisons. Although a portion of papers provides source code, they adopted different programming languages or different deep learning packages, which also raises the bar in grasping the ideas. To alleviate this problem, we released the open source project: . In this toolkit, we have implemented a number of deep learning based recommendation algorithms using Python and the widely used deep learning package - Tensorflow. Three major recommendation scenarios: rating prediction, top-N recommendation (item ranking) and sequential recommendation, were considered. Meanwhile, DeepRec maintains good modularity and extensibility to easily incorporate new models into the framework. It is distributed under the terms of the GNU General Public License. The source code is available at github: this https URL