Matrix approximation (MA) is one of the most popular techniques in today's recommender systems. In most MA-based recommender systems, the problem of risk minimization should be defined, and how to achieve minimum expected risk in model learning is one of the most critical problems to recommendation accuracy. This paper addresses the expected risk minimization problem, in which expected risk can be bounded by the sum of optimization error and generalization error. Based on the uniform stability theory, we propose an expected risk minimized matrix approximation method (ERMMA), which is designed to achieve better tradeoff between optimization error and generalization error in order to reduce the expected risk of the learned MA models. Theoretical analysis shows that ERMMA can achieve lower expected risk bound than existing MA methods. Experimental results on the MovieLens and Netflix datasets demonstrate that ERMMA outperforms six state-of-the-art MA-based recommendation methods in both rating prediction problem and item ranking problem.

With the advance of acquisition techniques, plentiful higherorder tensor data sets are built up in a great variety of fields such as computer vision, neuroscience, remote sensing and recommender systems. The real-world tensors often contain missing values, which makes tensor completion become a prerequisite to utilize them. Previous studies have shown that imposing a low-rank constraint on tensor completion produces impressive performances. In this paper, we argue that low-rank constraint, albeit useful, is not effective enough to exploit the local smooth and piecewise priors of visual data. We propose integrating total variation into low-rank tensor completion (LRTC) to address the drawback. As LRTC can be formulated by both tensor unfolding and tensor decomposition, we develop correspondingly two methods, namely LRTC-TV-I and LRTC-TVII, and their iterative solvers. Extensive experimental results on color image and medical image inpainting tasks show the effectiveness and superiority of the two methods against state-of-the-art competitors.

Recommender systems have achieved great success in recent years, and matrix approximation (MA) is one of the most popular techniques for collaborative filtering (CF) based recommendation. However, a major issue is that MA methods perform poorly at detecting strong localized associations among closely related users and items. Recently, some MA-based CF methods adopt clustering methods to discover meaningful user-item subgroups and perform ensemble on different clusterings to improve the recommendation accuracy. However, ensemble learning suffers from lower efficiency due to the increased overall computation overhead. In this paper, we propose GLOMA, a new clustering-based matrix approximation method, which can embed global information in local matrix approximation models to improve recommendation accuracy. In GLOMA, a MA model is first trained on the entire data to capture global information. The global MA model is then utilized to guide the training of cluster-based local MA models, such that the local models can detect strong localized associations shared within clusters and at the same time preserve global associations shared among all users/items. Evaluation results using MovieLens and Netflix datasets demonstrate that, by integrating global information in local models, GLOMA can outperform five state-of-the-art MA-based CF methods in recommendation accuracy while achieving descent efficiency.

Personalized ranking is usually considered as an ultimate goal of recommendation systems, but it suffers from efficiency issues when making recommendations. To this end, we propose a learning-based hashing framework called Discrete Personalized Ranking (DPR), to map users and items to a Hamming space, where user-item affinity can be efficiently calculated via Hamming distance. Due to the existence of discrete constraints, it is possible to exploit a two-stage learning procedure for learning binary codes according to most existing methods. This two-stage procedure consists of relaxed optimization by discarding discrete constraints and subsequent binary quantization. However, such a procedure has been shown resulting in a large quantization loss, so that longer binary codes would be required. To this end, DPR directly tackles the discrete optimization problem of personalized ranking. And the balance and un-correlation constraints of binary codes are imposed to derive compact but informatics binary codes. Based on the evaluation on several datasets, the proposed framework shows consistent superiority to the competing baselines even though only using shorter binary code.

Feature hierarchy (FH) has proven to be effective to improve recommendation accuracy. Prior work mainly focuses on the influence of vertically affiliated features (i.e. child-parent) on user-item interactions. The relationships of horizontally organized features (i.e. siblings and cousins) in the hierarchy, however, has only been little investigated. We show in real-world datasets that feature relationships in horizontal dimension can help explain and further model user-item interactions. To fully exploit FH, we propose a unified recommendation framework that seamlessly incorporates both vertical and horizontal dimensions for effective recommendation. Our model further considers two types of semantically rich feature relationships in horizontal dimension, i.e. complementary and alternative relationships. Extensive validation on four real-world datasets demonstrates the superiority of our approach against the state of the art. An additional benefit of our model is to provide better interpretations of the generated recommendations.

We perform online interactive recommendation via a factorization-based bandit algorithm. Low-rank matrix completion is performed over an incrementally constructed user-item preference matrix, where an upper confidence bound based item selection strategy is developed to balance the exploit/explore trade-off during online learning. Observable contextual features and dependency among users (e.g., social influence) are leveraged to improve the algorithm's convergence rate and help conquer cold-start in recommendation. A high probability sublinear upper regret bound is proved for the developed algorithm, where considerable regret reduction is achieved on both user and item sides. Extensive experimentations on both simulations and large-scale real-world datasets confirmed the advantages of the proposed algorithm compared with several state-of-the-art factorization-based and bandit-based collaborative filtering methods.

In many applications such as recommender systems and multi-label learning the task is to complete a partially observed binary matrix. Such PU learning (positive-unlabeled) problems can be solved by one-class matrix factorization (MF). In practice side information such as user or item features in recommender systems are often available besides the observed positive user-item connections. In this work we consider a generalization of one-class MF so that two types of side information are incorporated and a general convex loss function can be used. The resulting optimization problem is very challenging, but we derive an efficient and effective alternating minimization procedure. Experiments on large-scale multi-label learning and one-class recommender systems demonstrate the effectiveness of our proposed approach.

Self-awareness is a crucial feature for a sociable agent or robot to better interact with humans. In a futuristic scenario, a conversational agent may occasionally be asked for its own opinion or suggestion based on its own thought, feelings, or experiences as if it is an individual with identity, personality, and social life. In moving towards that direction, in this paper, a brain inspired model of self-awareness is presented that allows an agent to learn to attend to different aspects of self as an individual with identity, physical embodiment, mental states, experiences, and reflections on how others may think about oneself. The model is built and realized on a NAO humanoid robotic platform to investigate the role of this capacity of self-awareness on the robot's learning and interactivity.

The cold-start problem involves recommendation of content to new users of a system, for whom there is no historical preference information available. This proves a challenge for collaborative filtering algorithms that inherently rely on such information. Recent work has shown that social metadata, such as users' friend groups and page likes, can strongly mitigate the problem. However, such approaches either lack an interpretation as optimising some principled objective, involve iterative non-convex optimisation with limited scalability, or require tuning several hyperparameters. In this paper, we first show how three popular cold-start models are special cases of a linear content-based model, with implicit constraints on the weights. Leveraging this insight, we propose Loco, a new model for cold-start recommendation based on three ingredients: (a) linear regression to learn an optimal weighting of social signals for preferences, (b) a low-rank parametrisation of the weights to overcome the high dimensionality common in social data, and (c) scalable learning of such low-rank weights using randomised SVD. Experiments on four real-world datasets show that Loco yields significant improvements over state-of-the-art cold-start recommenders that exploit high-dimensional social network metadata.

Graph Embedding methods are aimed at mapping each vertex into a low dimensional vector space, which preserves certain structural relationships among the vertices in the original graph. Recently, several works have been proposed to learn embeddings based on sampled paths from the graph, e.g., DeepWalk, Line, Node2Vec. However, their methods only preserve symmetric proximities, which could be insufficient in many applications, even the underlying graph is undirected. Besides, they lack of theoretical analysis of what exactly the relationships they preserve in their embedding space. In this paper, we propose an asymmetric proximity preserving (APP) graph embedding method via random walk with restart, which captures both asymmetric and high-order similarities between node pairs. We give theoretical analysis that our method implicitly preserves the Rooted PageRank score for any two vertices. We conduct extensive experiments on tasks of link prediction and node recommendation on open source datasets, as well as online recommendation services in Alibaba Group, in which the training graph has over 290 million vertices and 18 billion edges, showing our method to be highly scalable and effective.