More Like this

1. Fast Connectivity Minimization on Large-Scale Networks

   https://doi.org/10.1145/3442342  

   Chen, Chen; Peng, Ruiyue; Ying, Lei; Tong, Hanghang (May 2021, ACM Transactions on Knowledge Discovery from Data)

   null (Ed.)

   The connectivity of networks has been widely studied in many high-impact applications, ranging from immunization, critical infrastructure analysis, social network mining, to bioinformatic system studies. Regardless of the end application domains, connectivity minimization has always been a fundamental task to effectively control the functioning of the underlying system. The combinatorial nature of the connectivity minimization problem imposes an exponential computational complexity to find the optimal solution, which is intractable in large systems. To tackle the computational barrier, greedy algorithm is extensively used to ensure a near-optimal solution by exploiting the diminishing returns property of the problem. Despite the empirical success, the theoretical and algorithmic challenges of the problems still remain wide open. On the theoretical side, the intrinsic hardness and the approximability of the general connectivity minimization problem are still unknown except for a few special cases. On the algorithmic side, existing algorithms are hard to balance between the optimization quality and computational efficiency. In this article, we address the two challenges by (1) proving that the general connectivity minimization problem is NP-hard and is the best approximation ratio for any polynomial algorithms, and (2) proposing the algorithm CONTAIN and its variant CONTAIN + that can well balance optimization effectiveness and computational efficiency for eigen-function based connectivity minimization problems in large networks. 

   more » « less
2. iNEAT: Incomplete Network Alignment

   https://doi.org/10.1109/ICDM.2017.160  

   Zhang, Si; Tong, Hanghang; Tang, Jie; Xu, Jiejun; Fan, Wei (November 2017, IEEE ICDM)

   Network alignment and network completion are two fundamental cornerstones behind many high-impact graph mining applications. The state-of-the-arts have been addressing these tasks in parallel. In this paper, we argue that network alignment and completion are inherently complementary with each other, and hence propose to jointly address them so that the two tasks can benefit from each other. We formulate it from the optimization perspective, and propose an effective algorithm iNEAT to solve it. The proposed method offers two distinctive advantages. First (Alignment accuracy), our method benefits from higher-quality input networks while mitigates the effect of incorrectly inferred links introduced by the completion task itself. Second (Alignment efficiency), thanks to the low-rank structure of the complete networks and alignment matrix, the alignment can be significantly accelerated. The extensive experiments demonstrate the performance of our algorithm. 

   more » « less
3. New Frontiers of Multi-Network Mining: Recent Developments and Future Trend

   https://doi.org/10.1145/3447548.3470801  

   Du, Boxin; Zhang, Si; Yan, Yuchen; Tong, Hanghang (July 2021, KDD)

   null (Ed.)

   Networks (i.e., graphs) are often collected from multiple sources and platforms, such as social networks extracted from multiple online platforms, team-specific collaboration networks within an organization, and inter-dependent infrastructure networks, etc. Such networks from different sources form the multi-networks, which can exhibit the unique patterns that are invisible if we mine the individual network separately. However, compared with single-network mining, multi-network mining is still under-explored due to its unique challenges. First ( multi-network models ), networks under different circumstances can be modeled into a variety of models. How to properly build multi-network models from the complex data? Second ( multi-network mining algorithms ), it is often nontrivial to either extend single-network mining algorithms to multi-networks or design new algorithms. How to develop effective and efficient mining algorithms on multi-networks? The objectives of this tutorial are to: (1) comprehensively review the existing multi-network models, (2) elaborate the techniques in multi-network mining with a special focus on recent advances, and (3) elucidate open challenges and future research directions. We believe this tutorial could be beneficial to various application domains, and attract researchers and practitioners from data mining as well as other interdisciplinary fields. 

   more » « less
4. On the Generalized Mean Densest Subgraph Problem: Complexity and Algorithms

   https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.9  

   Chandrasekaran, Karthekeyan; Chekuri, Chandra; Torres, Manuel R; Zhu, Weihao (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Kumar, Amit; Ron-Zewi, Noga (Ed.)

   Dense subgraph discovery is an important problem in graph mining and network analysis with several applications. Two canonical polynomial-time solvable problems here are to find a maxcore (subgraph of maximum min degree) and to find a densest subgraph (subgraph of maximum average degree). Both of these problems can be solved in polynomial time. Veldt, Benson, and Kleinberg [Veldt et al., 2021] introduced the generalized p-mean densest subgraph problem which captures the maxcore problem when p = -∞ and the densest subgraph problem when p = 1. They observed that for p ≥ 1, the objective function is supermodular and hence the problem can be solved in polynomial time. In this work, we focus on the p-mean densest subgraph problem for p ∈ (-∞, 1). We prove that for every p ∈ (-∞,1), the problem is NP-hard, thus resolving an open question from [Veldt et al., 2021]. We also show that for every p ∈ (0,1), the weighted version of the problem is APX-hard. On the algorithmic front, we describe two simple 1/2-approximation algorithms for every p ∈ (-∞, 1). We complement the approximation algorithms by exhibiting non-trivial instances on which the algorithms simultaneously achieve an approximation factor of at most 1/2. 

   more » « less
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. 

   more » « less