第13卷第3期 智能系统学报 Vol.13 No.3 2018年6月 CAAI Transactions on Intelligent Systems Jun.2018 D0:10.11992/tis.201710027 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20180404.1358.012.html 符号网络的局部标注特征与预测方法 苏晓萍，宋玉蓉2 (1.南京工业职业技术学院计算机与软件学院，江苏南京210046,2.南京邮电大学自动化学院，江苏南京 210003) 摘要：当复杂网络的边具有正、负属性时称为符号网络。符号为正表示两用户间具有相互信任（朋友）关系，相反， 符号为负表示不信任（敌对）关系。符号网络中的一个重要研究任务是给定部分观测的符号网络，预测未知符号。分 析发现，具有弱结构平衡特征的符号网络，其邻接矩阵呈现全局低秩性，在该特征下链路符号预测问题可以近似表达 为低秩矩阵分解问题。但基本低秩模型中，相邻节点间符号标注的局部行为特征未得到充分利用，论文提出了一种 带偏置的低秩矩阵分解模型，将邻居节点的出边和入边符号特征作为偏置信息引入模型，以提高符号预测的精度。 利用真实符号网络数据进行的实验证明，所提模型能够获得较其他基准算法好的预测效果且算法效率高。 关键词：符号网络：符号预测：低秩：矩阵分解：标注偏置：结构平衡理论：弱结构平衡理论：地位理论 中图分类号：TP399文献标志码：A 文章编号：1673-4785(2018)03-0437-08 中文引用格式：苏晓萍，宋玉蓉.符号网络的局部标注特征与预测方法.智能系统学报，2018,13(3)：437-444. 英文引用格式：SU Xiaoping,SONG Yurong.Local labeling features and a prediction method for a signed networkJ.CAAI trans- actions on intelligent systems,2018,13(3):437-444. Local labeling features and a prediction method for a signed network SU Xiaoping SONG Yurong (1.School of Computer and Software Engineering,Nanjing Institute of Industry Technology,Nanjing 210046,China;2.College of Automation,Nanjing University of Posts and Telecommunications,Nanjing 210003,China) Abstract:A complex network may be considered as a symbol network when links have a positive or negative sign at- tribute.In signed social networks,positive links represent a trust(friends)relationship between users.In contrast,negat- ive links indicate distrust(hostility).An important task in a signed network is to define a signed network based on par- tial observation to predict an unknown symbol.Through analysis,we found that for a signed network with weak struc- tural balance,its adjacent matrix has a global low-rank characteristic and the prediction of the link sign can be approx- imated as a low-rank matrix factorization.However,in a basic low-rank model,it is difficult to sufficiently utilize the local behavior features for labeling the signs of links between the neighboring nodes.Herein,a low-rank matrix factoriz- ation model with bias was proposed.In this model,the sign features of the exit and entry links of a neighboring node were introduced to improve the precision of sign prediction.Experiments based on real data revealed that the low-rank model with bias can obtain better prediction results than other benchmark algorithms and that the proposed algorithm performed with a high efficiency. Keywords:signed networks;sign prediction;low rank;matrix factorization;signed bias;structural balance theory;weak structural balance theory;status theory 符号网络是指边具有正或负符号属性的网络， 收稿日期：2017-10-30.网络出版日期：2018-04-04。 基金项目：国家自然科学基金项目(61672298,61373136)：教育部 符号为正表示网络中两节点间具有相互信任的、积 人文社会科学研究规划基金项目(17 YJAZH071):江苏 省高校优秀科技创新团队项目. 极的朋友关系，负边则表示不信任的、消极的敌对 通信作者：苏晓萍.E-mail:419033424@qq.com. 关系。具有符号属性的网络普遍存在，研究链路DOI: 10.11992/tis.201710027 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20180404.1358.012.html 符号网络的局部标注特征与预测方法 苏晓萍1 ，宋玉蓉2 （1. 南京工业职业技术学院 计算机与软件学院，江苏 南京 210046; 2. 南京邮电大学 自动化学院，江苏 南京 210003） 摘 要：当复杂网络的边具有正、负属性时称为符号网络。符号为正表示两用户间具有相互信任 (朋友) 关系，相反， 符号为负表示不信任 (敌对) 关系。符号网络中的一个重要研究任务是给定部分观测的符号网络，预测未知符号。分 析发现，具有弱结构平衡特征的符号网络，其邻接矩阵呈现全局低秩性，在该特征下链路符号预测问题可以近似表达 为低秩矩阵分解问题。但基本低秩模型中，相邻节点间符号标注的局部行为特征未得到充分利用，论文提出了一种 带偏置的低秩矩阵分解模型，将邻居节点的出边和入边符号特征作为偏置信息引入模型，以提高符号预测的精度。 利用真实符号网络数据进行的实验证明，所提模型能够获得较其他基准算法好的预测效果且算法效率高。 关键词：符号网络；符号预测；低秩；矩阵分解；标注偏置；结构平衡理论；弱结构平衡理论；地位理论 中图分类号：TP399 文献标志码：A 文章编号：1673−4785(2018)03−0437−08 中文引用格式：苏晓萍, 宋玉蓉. 符号网络的局部标注特征与预测方法[J]. 智能系统学报, 2018, 13(3): 437–444. 英文引用格式：SU Xiaoping, SONG Yurong. Local labeling features and a prediction method for a signed network[J]. CAAI trans￾actions on intelligent systems, 2018, 13(3): 437–444. Local labeling features and a prediction method for a signed network SU Xiaoping1 ，SONG Yurong2 (1. School of Computer and Software Engineering, Nanjing Institute of Industry Technology, Nanjing 210046, China; 2. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China) Abstract: A complex network may be considered as a symbol network when links have a positive or negative sign at￾tribute. In signed social networks, positive links represent a trust (friends) relationship between users. In contrast, negat￾ive links indicate distrust (hostility). An important task in a signed network is to define a signed network based on par￾tial observation to predict an unknown symbol. Through analysis, we found that for a signed network with weak struc￾tural balance, its adjacent matrix has a global low-rank characteristic and the prediction of the link sign can be approx￾imated as a low-rank matrix factorization. However, in a basic low-rank model, it is difficult to sufficiently utilize the local behavior features for labeling the signs of links between the neighboring nodes. Herein, a low-rank matrix factoriz￾ation model with bias was proposed. In this model, the sign features of the exit and entry links of a neighboring node were introduced to improve the precision of sign prediction. Experiments based on real data revealed that the low-rank model with bias can obtain better prediction results than other benchmark algorithms and that the proposed algorithm performed with a high efficiency. Keywords: signed networks; sign prediction; low rank; matrix factorization; signed bias; structural balance theory; weak structural balance theory; status theory 符号网络是指边具有正或负符号属性的网络， 符号为正表示网络中两节点间具有相互信任的、积 极的朋友关系，负边则表示不信任的、消极的敌对 关系。具有符号属性的网络普遍存在[1] ，研究链路 收稿日期：2017−10−30. 网络出版日期：2018−04−04. 基金项目：国家自然科学基金项目 (61672298，61373136)；教育部 人文社会科学研究规划基金项目 (17YJAZH071)；江苏 省高校优秀科技创新团队项目. 通信作者：苏晓萍. E-mail: 419033424@qq.com. 第 13 卷第 3 期 智 能 系 统 学 报 Vol.13 No.3 2018 年 6 月 CAAI Transactions on Intelligent Systems Jun. 2018