A Semi-supervised Clustering Algorithm Based on Factor Graph Model for Dynamic Graphs
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摘要: 针对动态图的聚类主要存在着两点不足:首先, 现有的经典聚类算法大多从静态图分析的角度出发, 无法对真实网络图持续演化的特性进行有效建模, 亟待对动态图的聚类算法展开研究, 通过对不同时刻图快照的聚类结构进行分析进而掌握图的动态演化情况.其次, 真实网络中可以预先获取图中部分节点的聚类标签, 如何将这些先验信息融入到动态图的聚类结构划分中, 从而向图中的未标记节点分配聚类标签也是本文需要解决的问题.为此, 本文提出进化因子图模型(Evolution factor graph model, EFGM)用于解决动态图节点的半监督聚类问题, 所提EFGM不仅可以捕获动态图的节点属性和边邻接属性, 还可以捕获节点的时间快照信息.本文对真实数据集进行实验验证, 实验结果表明EFGM算法将动态图与先验信息融合到一个统一的进化因子图框架中, 既使得聚类结果满足先验知识, 又契合动态图的整体演化规律, 有效验证了本文方法的有效性.Abstract: There are two main deficiencies on clustering of dynamic graphs. Firstly, most of existing classical algorithms analyze such graphs from the perspective of static analysis. However, static analysis is not capable of modeling the continuous evolution of real-world networks. Therefore, it is a great need to research on clustering algorithms for dynamic graphs. Our goal is to capture the dynamic evolution characteristics by considering the clustering structure of multiple snapshots as a whole. Secondly, some clustering labels of some nodes in real-world graphs can be obtained in advance, thus how to integrate these priori information into clustering assignments of dynamic graphs and assign clustering labels to the unlabeled nodes of each snapshot should be resolved. In this paper, we propose an evolution factor graph model (EFGM) for the semi-supervised clustering of nodes in dynamic networks. EFGM is able to capture the node-attribute and edge-adjacency attribute of each node of the dynamic graphs, and also make full use of the snapshot information. We experiment with the real-world graphs and experimental results show that the EFGM integrates the prior knowledge and the dynamic graph into a unified framework (i.e., evolution factor graph model), which makes the clustering result satisfy the prior label information and conform to the overall evolution of dynamic graphs. It validates the effectiveness of the proposed approach.
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Key words:
- Semi-supervised clustering /
- evolution factor graph model (EFGM) /
- feature extraction /
- dynamic graphs
1) 本文责任编委 朱军 -
表 1 相关符号说明
Table 1 Description of symbols
符号 说明 $G_L $ 部分标注网络 $V_L $ 被标注的节点 $V_U $ 未被标注的节点 $E$ 图中的边集合 $W$ $W_{ij} $为节点$V_i $的第$j_{th} $个属性值 $f$ 映射函数, 将每个节点$i$赋予相应的标签, 记为$f_i$ $\Omega $ 部分标注动态网络 
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表 2 DBLP数据集的会议名称和聚类簇标签
Table 2 Conference names and their clustering labels of DBLP dataset
聚类簇标签 会议名称 AI & ML IJCAI, AAAI, ICML, UAI, AISTATS AL & TH FOCS, STOC, SODA, COLT CV CVPR, ICCV, ECCV, BMVC DB EDBT, ICDE, PODS, SIGMOD, VLDB DM KDD, SDM, ICDM, PAKDD IR SIGIR, ECIR
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表 3 DBLP会议论文网络的统计信息
Table 3 Statistics of DBLP conference network
年份 作者关系 关系数量 2001 3 074 5 743 2002 2 557 5 343 2003 3 836 7 700 2004 3 464 7 132 2005 5 198 11 171 2006 4 494 9 392 2007 7 294 15 708 2008 5 780 12 398 2009 6 405 14 321 2010 5 757 12 738
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表 4 真实网络图的实验结果比较
Table 4 Comparison of results on real-world graphs
网络集 相应算法 NMI RE HEPCitation EFGM 0.845 0.203 FFGM 0.393 0.478 CFGM 0.824 0.245 MV 0.578 0.450 SVM 0.502 0.423 DBLP EFGM 0.885 0.196 FFGM 0.493 0.280 CFGM 0.814 0.235 MV 0.678 0.350 SVM 0.560 0.323
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表 5 各个算法在真实网络数据集上的处理时间比较(秒)
Table 5 Comparison of the execution time on a real-world networks (s)
运行时间(s) EFGM FFGM CFGM MV SVM HEPCitation 282.8 269.2 272.6 220.3 394.4 DBLP 123.8 110.3 108.2 84 232.3
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表 6 不同特征提取方法的实验结果比较
Table 6 Comparison of results on different feature extraction methods
特征提取方法 NMI RE ReFeX EFGM 0.837 0.222 FFGM 0.372 0.427 CFGM 0.799 0.253 Node2vec EFGM 0.852 0.193 FFGM 0.402 0.392 CFGM 0.819 0.235
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