This paper proposes a novel scalable community-based neural framework for graph learning. The framework learns the graph topology through the task of community detection and link prediction by optimizing with our proposed joint SBM loss function, which results from a non-trivial adaptation of the likelihood function of the classic Stochastic Block Model (SBM). Compared with SBM, our framework is flexible, naturally allows soft labels and digestion of complex node attributes. The main goal is efficient valuation of complex graph data, therefore our design carefully aims at accommodating large data, and ensures there is a single forward pass for efficient evaluation. For large graph, it remains an open problem of how to efficiently leverage its underlying structure for various graph learning tasks. Previously it can be heavy work. With our community-based framework, this becomes less difficult and allows the task models to basically plug-in-and-play and perform joint training. We currently look into two particular applications, the graph alignment and the anomalous correlation detection, and discuss how to make use of our framework to tackle both problems. Extensive experiments are conducted to demonstrate the effectiveness of our approach. We also contributed tweaks of classic techniques which we find helpful for performance and scalability. For example, 1) the GAT+, an improved design of GAT (Graph Attention Network), the scaled-cosine similarity, and a unified implementation of the convolution/attention based and the random-walk based neural graph models.
Networks are ubiquitous in today's world. Community structure is a well-known feature of many empirical networks, and a lot of statistical methods have been developed for community detection. In this paper, we consider the problem of community structure in text networks,which is greatly relevant in medical errors and patient safety databases. We adapt a well-known community extraction method to develop a scalable algorithm for community extraction in large text databases. The application of our method on a real-world patient safety report database demonstrates that the groups generated from co…
University of Washington（华盛顿大学）；University of California, San Diego（加州大学圣地亚哥分校）
We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of two blocks: above the threshold, there is a spectral algorithm which asymptotically almost surely constructs a partition of the hypergraph correlated with the true partition. Our method is a generalization to random hypergraphs of the method developed by Massoulié (2014) for spa…
Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models
Graduate School of Systems Design, Tokyo Metropolitan University（东京 Metropolitan 大学系统设计研究生院）；Principles of Informatics Research Division, National Institute of Informatics（国家信息研究所信息原理研究部门）
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graph's adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clu…
University of Colorado（科罗拉多大学）；BioFrontiers Institute（生物前沿研究所）
In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in…
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio)（里约热内卢天主教大学）
The Degree-Corrected Stochastic Block Model (DCSBM) is a popular model to generate random graphs with community structure given an expected degree sequence. The standard approach of community detection based on the DCSBM is to search for the model parameters that are the most likely to have produced the observed network data through maximum likelihood estimation (MLE). Current techniques for the MLE problem are heuristics, and therefore do not guarantee convergence to the optimum. We present mathematical programming formulations and exact solution methods that can provably find the model param…
Graph clustering and community detection are central problems in modern data mining. The increasing need for analyzing billion-scale data calls for faster and more scalable algorithms for these problems. There are certain trade-offs between the quality and speed of such clustering algorithms. In this paper, we design scalable algorithms that achieve high quality when evaluated based on ground truth. We develop a generalized sequential and shared-memory parallel framework based on the LambdaCC objective (introduced by Veldt et al.), which encompasses modularity and correlation clustering. Our f…
The University of California at Los Angeles（加利福尼亚大学洛杉矶分校）；Federal University of Rio de Janeiro（里约热内卢联邦大学）；The University of Notre Dame（圣母大学）
Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In cont…
We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic in the number of vertices. Our main result derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs. This threshold captures the interplay between the community recovery and graph matching tasks. In particular, we uncover and characterize a region of the parameter space where exact community recovery …
Johns Hopkins University（约翰斯·霍普金斯大学）；University of Pittsburgh（匹兹堡大学）
In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity. Beyond mere adjacency matrices, many real networks also involve vertex covariates that carry key information about underlying block structure in graphs. To assess the effects of such covariates on block recovery, we present a comparative analysis of two model-based spectral algorithms for clustering vertices in stochastic blockmodel graphs with vertex covariates. The first algorithm uses only the adjacency matrix, an…
Virginia Tech（弗吉尼亚理工大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）
Community detection is a well-studied problem with applications in domains ranging from networking to bioinformatics. Due to the rapid growth in the volume of real-world data, there is growing interest in accelerating contemporary community detection algorithms. However, the more accurate and statistically robust methods tend to be hard to parallelize. One such method is stochastic block partitioning (SBP) - a community detection algorithm that works well on graphs with complex and heterogeneous community structure. In this paper, we present a sampling-based SBP (SamBaS) for accelerating SBP o…
Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be specified in advance. In this article, a novel Bayesian mo…
Universal Phase Transition in Community Detectability under a Stochastic Block Model
我们证明了谱模块化方法中社区可检测性的渐近相变阈值的存在性[M。E. J.Newman，Phys.Rev.E74，036104（2006）和Proc.National Academy of Sciences. 103，8577（2006）]中的随机块模型。随着社区间边缘连接概率$p$的增长，社区可检测性发生相变。该相变将小$p$的次临界状态（其中基于模块的社区检测成功地识别社区）与大$p$的超临界状态（其中成功的社区发现是不可能的）分开。我们发现，随着社区规模变大，渐近相变阈值$p^*$等于$\sqrt{p_1\cdot p_2}$，其中$p_i~(i=1,2)$是社区内边缘连接概率。因此，相变阈值是普遍的，在这个意义上，它不依赖于社区大小的比例。通过对中等规模社区的模拟，验证了普遍的相变现象。使用推导出的相变阈值的表达式，我们提出了一个经验的方法来估计这个阈值从现实世界的数据。
In this work, we consider community detection in blockchain networks. We specifically take the Bitcoin network and Ethereum network as two examples, where community detection serves in different ways. For the Bitcoin network, we modify the traditional community detection method and apply it to the transaction social network to cluster users with similar characteristics. For the Ethereum network, on the other hand, we define a bipartite social graph based on the smart contract transactions. A novel community detection algorithm which is designed for low-rank signals on graph can help find users…
We propose a dynamic network sampling scheme to optimize block recovery for stochastic blockmodel (SBM) in the case where it is prohibitively expensive to observe the entire graph. Theoretically, we provide justification of our proposed Chernoff-optimal dynamic sampling scheme via the Chernoff information. Practically, we evaluate the performance, in terms of block recovery, of our method on several real datasets from different domains. Both theoretically and practically results suggest that our method can identify vertices that have the most impact on block structure so that one can only chec…
We introduce a novel model for multilayer weighted networks that accounts for global noise in addition to local signals. The model is similar to a multilayer stochastic blockmodel (SBM), but the key difference is that between-block interactions independent across layers are common for the whole system, which we call ambient noise. A single block is also characterized by these fixed ambient parameters to represent members that do not belong anywhere else. This approach allows simultaneous clustering and typologizing of blocks into signal or noise in order to better understand their roles in the…
Active Learning for Community Detection in Stochastic Block Models
University of Southern California（南加州大学）
随机块模型（SBM）是网络科学和机器学习中随机图的一个重要生成模型，可用于基准测试社区发现（或聚类）算法。对称SBM生成具有$2n$节点的图，这些节点聚类成两个相等大小的社区。节点在社区内以概率$p$连接，在不同社区之间以概率$q$连接。我们考虑$p=a\ln (n)/n$和$q=b\ln (n)/n$的情况。在这种情况下，最近表明，以高概率（w. h. p.）仅使用该图是可能的，当且仅当B-H（CH）发散$D(a,b)=(\sqrt{a}-\sqrt{b})^2 \geq 1$。在这项工作中，我们研究了社区发现查询有限数量的所选节点的标签（即，主动学习）。我们的主要结果是表明，在一定条件下，采样标签的一个消失的小部分节点（一个数字次线性$n$）是足够的精确社区发现，即使当$D(a,b)<1$。此外，我们提供了一个有效的学习算法，恢复社区成员的所有节点w. h. p.，只要采样点的数量满足充分条件。我们还表明，恢复是不可能的，如果观察到的标签的数量小于$n^{1-D(a,b)}$。通过数值实验证明了我们的结果的有效性。
Community structure is one of the most important features of complex networks. Modularity-based methods for community detection typically rely on heuristic algorithms to optimize a specific community quality function. Such methods are limited by two major defects: (1) the resolution limit problem, which prohibits communities of heterogeneous sizes being simultaneously detected, and (2) divergent outputs of the heuristic algorithm, which make it difficult to differentiate relevant and irrelevant results. In this paper, we propose an improved method for community detection based on a scalable co…
Group testing was conceived during World War II to identify soldiers infected with syphilis using as few tests as possible, and it has attracted renewed interest during the COVID-19 pandemic. A long-standing assumption in the probabilistic variant of the group testing problem is that individuals are infected by the disease independently. However, this assumption rarely holds in practice, as diseases often spread through interactions between individuals and therefore cause infections to be correlated. Inspired by characteristics of COVID-19 and other infectious diseases, we introduce an infecti…
