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1. Time-sensitive POI Recommendation by Tensor Completion with Side Information

   Hui, Bo ; Yan, Da ; Ku, Wei-Shinn ( January 2022 , Proceedings of the 38th IEEE International Conference on Data Engineering (ICDE))

   Context has been recognized as an important factor to consider in personalized recommender systems. Particularly in location-based services (LBSs), a fundamental task is to recommend to a mobile user where he/she could be interested to visit next at the right time. Additionally, location-based social networks (LBSNs) allow users to share location-embedded information with friends who often co-occur in the same or nearby points-of-interest (POIs) or share similar POI visiting histories, due to the social homophily theory and Tobler’s first law of geography. So, both the time information and LBSN friendship relations should be utilized for POI recommendation. Tensor completion has recently gained some attention in time-aware recommender systems. The problem decomposes a user-item-time tensor into low-rank embedding matrices of users, items and times using its observed entries, so that the underlying low-rank subspace structure can be tracked to fill the missing entries for time-aware recommendation. However, these tensor completion methods ignore the social-spatial context information available in LBSNs, which is important for POI recommendation since people tend to share their preferences with their friends, and near things are more related than distant things. In this paper, we utilize the side information of social networks and POI locations to enhance themore »tensor completion model paradigm for more effective time-aware POI recommendation. Specifically, we propose a regularization loss head based on a novel social Hausdorff distance function to optimize the reconstructed tensor. We also quantify the popularity of different POIs with location entropy to prevent very popular POIs from being over-represented hence suppressing the appearance of other more diverse POIs. To address the sensitivity of negative sampling, we train the model on the whole data by treating all unlabeled entries in the observed tensor as negative, and rewriting the loss function in a smart way to reduce the computational cost. Through extensive experiments on real datasets, we demonstrate the superiority of our model over state-of-the-art tensor completion methods.« less
2. Matrix Completion with Hierarchical Graph Side Information

   Elmahdy, Adell ; Ahn, Junhyung ; Suh, Changho ; Mohajer, Soheil ( January 2020 , Advances in neural information processing systems)

   We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.
3. Matrix Completion with Hierarchical Graph Side Information

   Elmahdy, Adel ; Ahn, Junhyung ; Suh, Changho ; Mohajer, Soheil ( January 2020 , Advances in neural information processing systems)

   We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.
4. Matrix Completion with Hierarchical Graph Side Information

   Elmahdy, Adel ; Ahn, Junhyung ; Suh, Changho ; Mohajer, Soheil ( January 2020 , Advances in neural information processing systems)

   We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.
5. A Harmonic Extension Approach to Collaborative Ranking

   Kuang, Da ; Shi, Zuoqiang ; Osher, Stanley ; Bertozzi, Andrea L ( December 2017 , International Symposium on Nonlinear Theory and its Applications)

   We present a new perspective on graph based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank approximation methods using convex optimization and the nuclear norm, we formulate matrix completion as a series of semi-supervised learning problems, and propagate the known ratings to the missing ones on the user-user or item-item graph globally. The semi-supervised learning problems are expressed as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and can be discretized by a point integral method. Our approach, named LDM (low dimensional manifold), does not impose a low-rank Euclidean subspace on the data points, but instead minimizes the dimension of the underlying manifold. It turns out to be particularly effective in generating rankings of items, showing decent computational efficiency and robust ranking quality compared to state-of-the-art methods.