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1. Matrix Completion with Hierarchical Graph Side Information

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

   null (Ed.)

   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. 

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2. Matrix Completion with Hierarchical Graph Side Information

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

   null (Ed.)

   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. 

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3. The Optimal Sample Complexity of Matrix Completion with Hierarchical Similarity Graphs

   https://doi.org/10.1109/ISIT50566.2022.9834449  

   Elmahdy, Adel ; Ahn, Junhyung ; Mohajer, Soheil ; Suh, Changho ( January 2022 , 2022 IEEE International Symposium on Information Theory (ISIT))

   We study a matrix completion problem that lever-ages a hierarchical structure of social similarity graphs as side information in the context of recommender systems. We assume that users are categorized into clusters, each of which comprises sub-clusters (or what we call “groups”). We consider a low-rank matrix model for the rating matrix, and a hierarchical stochastic block model that well respects practically-relevant social graphs.Under this setting, we characterize the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) as a function of the quality of graph side information (to be detailed) by proving sharp upper and lower bounds on the sample complexity. Furthermore, we develop a matrix completion algorithm and empirically demonstrate via extensive experiments that the proposed algorithm achieves the optimal sample complexity. 

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4. Node-Polysemy Aware Recommendation by Matrix Completion with Side Information

   https://doi.org/10.1109/BigData52589.2021.9672000  

   Hui, Bo ; Yan, Da ; Ku, Wei-Shinn ( January 2021 , 2021 IEEE International Conference on Big Data (Big Data))

   Matrix completion is a well-known approach for recommender systems. It predicts the values of the missing entries in a sparse user-item interaction matrix, based on the low-rank structure of the rating matrix. However, existing matrix completion methods do not take node polysemy and side information of social relationships into consideration, which can otherwise further improve the performance. In this paper, we propose a novel matrix completion method that employs both users’ friendships and rating entries to predict the missing values in a user-item matrix. Our approach adopts a graph-based modeling where nodes are users and items, and two types of edges are considered: user friendships and user-item interactions. Polysemy-aware node features are extracted from this heterogeneous graph through a graph convolution network by considering the multifaceted factors for edge formation, which are then connected to a hybrid loss function with two heads: (1) a social-homophily head to address node polysemy, and (2) an error head for user-item rating regression. The latter is formulated on all matrix entries to combat the sensitivity of negative sampling of the vast majority of missing entries during training, with a smart technique to reduce the time complexity. Extensive experiments over real datasets verify that our model outperforms the state-of-the-art matrix completion methods by a significant margin. 

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5. N2N: Network Derivative Mining

   https://doi.org/10.1145/3357384.3357910  

   Kang, Jian ; Tong, Hanghang ( November 2019 , CIKM)

   Network mining plays a pivotal role in many high-impact application domains, including information retrieval, healthcare, social network analysis, security and recommender systems. State-of-the-art offers a wealth of sophisticated network mining algorithms, many of which have been widely adopted in real-world with superior empirical performance. Nonetheless, they often lack effective and efficient ways to characterize how the results of a given mining task relate to the underlying network structure. In this paper, we introduce network derivative mining problem. Given the input network and a specific mining algorithm, network derivative mining finds a derivative network whose edges measure the influence of the corresponding edges of the input network on the mining results. We envision that network derivative mining could be beneficial in a variety of scenarios, ranging from explainable network mining, adversarial network mining, sensitivity analysis on network structure, active learning, learning with side information to counterfactual learning on networks. We propose a generic framework for network derivative mining from the optimization perspective and provide various instantiations for three classic network mining tasks, including ranking, clustering, and matrix completion. For each mining task, we develop effective algorithm for constructing the derivative network based on influence function analysis, with numerous optimizations to ensure a linear complexity in both time and space. Extensive experimental evaluation on real-world datasets demonstrates the efficacy of the proposed framework and algorithms. 

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