电子商务翻译

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Electronic Commerce Research and Applications

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电子商务研究与应用

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Discovering target groups in social networking sites: An effective method for maximizing joint in?uential power

在社交网站中发现目标群体：一种有效的方法为最大限度地发挥联合的影响力

With the tremendous popularity of social networking sites in this era of Web 2.0, increasingly more usersare contributing their comments and opinions about products, people, organizations, and many otherentities. These online comments often have direct in?uence on consumers’ buying decisions and the pub-lic’s impressions of enterprises. As a result, enterprises have begun to explore the feasibility of usingsocial networking sites as platforms to conduct targeted marking and enterprise reputation managementfor e-commerce and e-business. As indicated from recent marketing research, the joint in?uential powerof a sm all group of active users could have considerable impact on a large number of consumers’ buyingdecisions and the public’s perception of the capabilities of enterprises. This paper illustrates a novelmethod that can effectively discover the most in?uential users from social networking sites (SNS). In par-ticular, the general method of mining the in?uence network from SNS and the computational models ofmathematical programming for discovering the user groups with max joint in?uential power are pro-posed. The empirical evaluation with real data extracted from social networking sites shows that the pro-posed method can effectively identify the most in?uential groups when compared to the benchmarkmethods. This study opens the door to effectively conducting targeted marketing and enterprise reputa-tion management on social networking sites.

随着广受欢迎的社交网站在这个Web 2.0时代，越来越多的用户有关产品，人员，组织，和许多其他贡献自己的意见和建议的实体。这些网上的意见往往直接影响消费者的购买决策和酒吧LIC的企业的印象。其结果是，企业已经开始探索使用的可行性社交网站平台，进行有针对性的标志和企业声誉管理电子商务和电子商务。正如从最近的市场调研，联合影响力一小群的活跃用户，可以有相当大的影响消费者的购买大量的决策和公众的认知能力的企业。本文阐述了一种新型的方法，可以有效地发现最有影响力的社交网站（SNS）的用户。在PAR-特别地，开采的影响从SNS的网络的一般方法，和计算模型发现的用户群体最大的联合影响力的数学规划是亲构成的。从社交网站中提取的真实数据的实证评价表明，亲构成的方法可以有效地识别最有影响力的群体相比基准的方法。这项研究打开大门，有效地进行有针对性的营销和企业声誉在社交网站上的重刑管理。

随着Web 2.0时代的到来，社交类网站越来越受到欢迎，越来越多的产品，组织，人员，和许多其他用户把自己的意见和建议实施和添加到这个实体中。这些社交类网站上的意见往往直接影响消费者的购买决策和对于LIC的企业的印象。其导致的结果，就是企业已经开始探索开发和使用自己的可行性社交网站平台，在电子商务中进行有针对性的和对于企业声誉有关的管理。最近的市场调研显示，联合一小群有影响力的活跃用户，可以在相当大的程度上影响消费者的购买决策，文阐述了一种新型的方法，可以有效地发现最有影响力的社交网站（SNS）的用户。特别的，从SNS的网络提起的有一定影响的开发方法，与利用计算机模型发现的最大的且具有强力影响力的用户群体有相互关系。从社交网站中提取的真实且具有实证评价的数据表明，亲构成的方法可以有效地识别最有影响力的群体相比的方法。这项研究有效地打开了有针对性的营销和在社交网站上的管理企业声誉的大门。

1. Introduction

1。介绍

In this Web 2.0 era, users are able to express their opinions onproducts through many channels such as online forums, shoppingwebsites, blogs, and wikis. These opinions can in?uence otherusers’ buying decisions and their views on companies (Cheunget al. 2009, Chevalier andMayzlin 2006, Dellarocas 2003,Hennig-Thurau and Walsh 2003, Koh et al. 2010, Mayzlin 2006,Park et al. 2007). Recently, the emerging channel of social network-ing sites (SNS), such asFacebook, Twitter, and Epinions, has at-tracted the attention of marketing practitioners and researchers.These sites not only permit users to express comments and opin-ions on products, people, organizations, and many other entities,but also enables users to build various social relationships. Forexample, on the Epinions site (Epinions 2010), a user can build atrust relationship with another by adding him or her to a trust list,or the user can block him or her with a block list. The site thenshows the trusted users’ opinions at the top of the list. With thesesocial relationships,

在这个Web2.0时代，用户可以表达自己的意见产品通过多种渠道，如网上论坛，购物网站，博客和维基。这些意见可以影响其他用户的购买决策，他们的意见对公司（长安等人。2009年，富安，2003年Dellarocas2006年Mayzlin的Hennig图劳和沃尔什2003年，苏梅等。20102006年Mayzlin，Park等人。2007年）。最近，新兴的社交网络渠道（SNS）网站，如Facebook，Twitter和Epinions-牙牙营销从业者和研究者的关注。这些网站不仅允许用户表达意见和奥平离子对产品，人员，组织，和许多其他实体，但也使用户能够建立各种社会关系。为的的Epinions网站（Epinions2010）上，例如，用户可以建立一个信任关系与另一个他或她加入到信任列表，或者用户可以阻止他或她的阻止列表。然后该网站显示在列表顶部的受信任的用户的意见。与这些社会关系，

pinions will have greater impact on usersthan those expressed on the other channels (such as shoppingwebsites) because people always believe or accept more easilythe opinions of those with whom they have social relationships(Golbeck 2005, Lu et al. 2010, Massa and Avesani 2007). In addi-tion, the in?uence of opinions on SNS can be disseminated morewidely and quickly than that of other channels. Thus, some users’opinions captured on SNS can greatly in?uence other users’ buyingdecisions or their views on certain companies.

Many business entities have recently come to recognize thisphenomenon, and some companies have begun to identify certainusers of SNS to conduct online marketing and reputation manage-ment (Conlin and MacMillan 2010, Marks 2010, Miller and Dickson2001) in e-commerce and e-business. For companies to better uti-lize SNS for cost-effective, targeted marketing and reputation man-agement, they must address an important question, given the hugenumber of social network users a nd companies’ limited budgets.That brings us to the question of which users’ opinions will most in?uence others’ actions. If the most in?uential group of userscould be identi?ed, companies could consume minimal resourcesto improve product sales and enhance their reputations.

齿轮将有更大的影响所表达usersthan对其他渠道（如shoppingwebsites）的，因为人们总是相信或接受更easilythe的那些与他们有社会关系（Golbeck2005年，鲁等人，2010年，马萨和2007年Avesani的意见）。此外，SNS 上的意见，能散发morewidely和速度比其他渠道影响。因此，一些SNS上拍摄的users'opinions可以大大影响其他用户的buyingdecisions对某些公司或他们的意见。

最近许多商业实体已经认识到寻找这个状况，一些公司已开始物色SNS certainusers的，在电子商务和电子商务开展网络营销和声誉管理（康林和麦克米伦2010年，2010年商标，米勒和Dickson2001的）。对于符合成本效益的，有针对性的营销和声誉的人管理公司，以更好地利用丽泽SNS，他们必须解决的一个重要问题，鉴于社交网络用户和公司的有限budgets.That hugenumber给我们带来了哪些用户的问题“意见mostinfluence他人的行为。如果最有影响力的一群userscould被确定，企业可以消耗最少resourcesto的提高产品销售和提高自己的声誉。

Although there are many existing studies on measuring nodeimportance in social network analysis (Wasserman and Faust1994), as well as studies that explore the spread of in?uence in so- cial networks (Kempe et al. 2003, Kempe et al. 2005), these works emphasize the importance of each node, without considering thejoint in?u ential power of a group of nodes. According to the latest?ndings from marketing research (Katona et al. 2007, 2011), if thecustomers are provided with positive information on products orenterprises by all related users in online communities, there maybe a higher probability of customers purchasing such products orhaving positive perceptions of these enterprises. This is known asthe joint in?uential power of a group of users. Previous researchalso indicates that the joint in?uential power of a small group of users could have considerable impact on a large number of con-sumers (Domingos and Richardson 2001, Richardson and Domin-gos 2002). Therefore, marketing personnel should identify theusers who have great joint in?uential power on SNS, and ?nd waysto encoura ge these users to express positive opinions about com-panies and the companies’ products through the strategy oftargeted marketing. As a result, companies could maximally pro-mote product sales and improve enterprises’ reputations throughthe joint in?uential power of the speci?c group of users.

Effectively discovering the group of users with maximal jointin?uential power from the huge number of users on SNS has be-come a key issue for companies to conduct targeted marketingand reputation management. Although previous research hasexamined the problem of discovering a group of in?uential users,the heuristic method used does not address the issue of identifyinga group with maximal joint in?uential power (Zhang et al. 2008).One of the weaknesses of the previous research is that the usersare added into the target group one by one, according to theirattributes and parts of trust relationships between them, withoutconsidering the in?uential power of the target group as a whole.Thus, these method usually do not disc over target groups havingthe most joint in?uential power (Kempe et al. 2003). In contrast,our proposed method represents global in?uential relationshipsamong all users as a directed graph, and uses mathematical pro-gramming as the computational apparatus to discover the groupof users with maximal joint in?uential power. Considering the costof marketing, the proposed models can discover the target groupwith ?exible costs. The empirical evaluation with real data fromEpinions and Twitter websites shows that the proposed methodshows much better performances, compared to the benchmarkmethods. In summary, the main contribution of our research isthe development of a novel method that discovers the user groupwith maximal joint in?uential power in a cost-effective way; italso overcomes the disadvantage of existing methods (Zhanget al. 2008) which only consider the attributes of users and partsof in?uence relationship. Our research opens the door to applywidely available data captured on SNS to conduct targeted market-ing and enterprise reputation management in e-commerce ande-business.

虽然有许多现有的上测量nodeimportance研究在社交网络分析（Wasserman和Faust1994），以及研究，探索中的传播影响力，使的CIAL网络（肯普等人，2003年，肯普等，2005年），这些作品强调每个节点的重要性，而不考虑的影响力thejoint的一组节点。据从市场调研latestfindings（卡托纳等，2007年，2011年），，如果thecustomers提供所有相关用户在网上社区积极信息产品orenterprises的，有可能是概率较高的客户购买此类产品orhaving这些积极的看法企业。这被称为的联合asthe影响力的一组用户。上一页researchalso表示的联合影响力的一小群ofusers的可能有相当大的影响了一大批CON消费者（2001年多明戈斯和理查德森，理查德森和海德明-GOS 2002）。因此，营销人员应确定有很大的影响力联合对SNS的用户是想怎么样，找到waysto鼓励这些用户表达正面的意见，对公司和公司的产品通过战略oftargeted营销。因此，企业可以最大限度地促进产品销售和提高企业的声誉throughthe特定的用户群的

联合影响力。

有效地发现了一批的用户最大jointinfluential功率从SNS上的用户数量庞大的已来到进行有针对性marketingand的声誉管理公司的一个关键问题。虽然以前的研究第十一条的问题，发现了一批有影响力的用户，使用启发式方法不解决这个问题，identifyinga组联合有影响力的最大功率（Zhang等，2008）。在前人研究的弱点之一是，添加到目标群体之一usersare一，根据theirattributes和部分之间的信任关系，withoutconsidering作为一个whole.Thus目标群体的影响力，这些方法通常没有发现目标群体havingthe最共同的影响力（肯普等人，2003）。相反，我们提出的方法表示全球有影响力relationshipsamong的所有用户作为一个有向图，并使用数学计算设备发现groupof的联合影响力最大的用户编程。考虑costof营销，提出的模型可以发现目标groupwith的灵活的成本。实证评价与真正的数据fromEpinions和Twitter的网站显示，建议methodshows的更好的表演，到benchmarkmethods相比。综上所述，我们的研究“是一种新的方法，发现用户groupwith最大的联合影响力的具有成本效益的方式发展的主要贡献，它也克服了现有方法的缺点（人Zhanget 2008）只考虑属性用户和影响关系partsof。我们的研究开启了大门到applywidely SNS上捕获的数据进行有针对性的市场和企业声誉管理在电子商务安山岩业务。

The rest of the paper is organized as follows. Section 2 discussesrelated research. Section 3 provides an overview of the proposedmethod for cost-effective targeted marketing and enterprise repu-tation management. Section 4 presents the computational modelsfor discovering the most in?uential group s of users. Section 5 re-ports the experimental evaluation of the proposed method, andSection 6 summarizes our research work and discusses directionsfor future work.

剩下的纸张安排如下：第2 discussesrelated研究。第3节提供了一个符合成本效益的有针对性的市场营销和企业声誉的塔季翁管理概述proposedmethod。第4节提出了的计算modelsfor发现最有影响力的团体用户。第5端口的实验评估所提出的方法，andSection6总结了我们的研究工作，并讨论了今后的工作directionsfor。

2. Related work

2。相关工作

2.1. Target group

2.1。目标客户群

A few studies exist that involve discovering a target group, and these bear some similarity to this study. In (Zhang et al. 2008), an algorithm based on the trust relationships between users is pro-posed to detect the in?uential target groups. The users are ranked according to the number of their written reviews, and then the users and the trust relationships are sequentially added into the target group until the clustering coef?cient of the target group is less than a threshold. However, the clustering coef?cient only re-?ects the in?uence relationships of the users added into the group,without considering the in?uence of relationships outside the group. Thus, this method fails to consider the in?uential power of the target group as a whole, and it tends to discover target groups consisting of mutual in?uence users which do not always have the most joint in?uential power over other users (Kempe et al. 2003). Diverging from their method, our proposed method mines the in?uence relationships from SNS, represents them in a directed graph, and discovers the target group that has maximal joint in?uential power by exploring all in?uence relationships using the models of mathematical programming.

存在一些研究，包括发现目标群体，而这些有某些相似之处这项研究。（张等，2008），提出了一种基于用户之间的信任关系是亲对检测有影响力的目标群体。用户排名按照其书面评论的数量，然后依次加入到目标群体的目标群体是直到聚类系数小于阈值用户和信任关系。然而，聚类系数只有重新反映用户添加到该组的影响关系，而不考虑的影响外组的关系。因此，这种方法没有考虑到目标群体的影响力作为一个整体，它往往发现目标群体包括相互影响的用户并不总是有最联合的影响力比其他用户（肯普等，2003年）。发散他们的方法，我们提出的方法地雷的影响从SNS的关系，表示他们有向图中，发现目标群体，具有极大的影响力联合探索所有影响关系，利用数学规划模型。

2.2. Node importance

In social network analysis, centrality is proposed to measure the importance of one node, and the nodes with higher centrality will then in?uence others more greatly (Wasserman and Faust 1994). Among the centrality measures, degree centrality is the com-monly-used one for in?uence, which is de?ned as the number of links incident upon a node. Persons who have more ties to others within a network may have more chances to in?uence others. In an undirected social network, centrality value is the number of connections one person has. With a directed social network, there are two ways to measure centrality: centrality based on out-degree and centrality based on in-degree. Other evolved centrality mea-sures include closeness centrality (considering the distance factor) and betweenness centrality (considering the position factor). In addition, the importance of each reviewer on SNS is also identi?ed by mining the linguistic features (Li et al. 2010). However. These metrics consider the importance of only one node, and the joint in?uential power of a group of nodes is not accurately re?ected by their degree of centrality (Kempe et al. 2003). In contrast, our study discovers the group of users with maximal joint in?uential power to help companies to conduct online marketing and reputa-tion management.

2.2。节点的重要性

在社会网络分析中，中心提出测量的重要性的一个节点上，并和中心性较高的节点，然后将大大影响他人（1994年Wasserman和浮士德）。度中心的中心措施中，通常使用的影响力，它被定义为一个节点后入射的链接数量。谁拥有更多的关系网络内的其他人可能有更多的机会去影响别人。在一个无向社会网络，中心值是一个人所具有的连接的数量。随着向社交网络中，有两种方法来衡量中心性：度和中心度的基础上的中心地位。其他进化心性MEA确保包括接近中心（考虑距离因素）和中介中心（考虑位置因素）。此外，SNS上的重要性，每个审稿还确定了挖掘的语言特点（Li等人，2010年）。然而。这些度量考虑只在一个节点的重要性，并不能准确地反射度中心性（肯普等人，2003）的联合影响力的一组节点。相比之下，我们的研究发现最大的联合影响力，帮助企业开展网络营销和声誉管理的用户组。

2.3. Spread of in?uence

This problem was proposed initially by Pedro Domingos and Matt Richardson in (Domingos and Richardson 2001, Richardson and Domingos 2002), and various studies followed to improve upon this work. The purpose of these studies is to explore the spread of in?uence in online social networks, and to identify in?u-ential users activating other users to buy products. In (Domingos and Richardson 2001), a method based on Markov random ?eld is used to simulate the spread of in?uence. In (Even-Dar and Shapira 2007, Kempe et al. 2003, Kempe et al. 2005), the spread process of in?uence is described using the linear threshold model,independent cascade model, and voter model. In (Ben-Zwi et al.2009, Chen et al. 2009, Kimura et al. 2007), a number of ef?cient approximate algorithms are proposed for this problem. The in?u- ence of network structure is explored in (Galstyan et al. 2009);product buying under a competitive social network is analyzed in (Carnes et al. 2007). In addition, other work has focused on diffu-sion and social in?uence in marketing research. For example, an approach is proposed to identify the speci?c users who most in?u-ence others’ activities for advertising targeting and retention efforts (Trusov et al. 2010), Nair et al. (2010) explore the impact of social interactions and measure the value of in?uential users in directing targeted sales; a marketing strategy for maximizing revenues is studied in (Hartline et al. 2008).

In contrast to these works, our study focuses on discovering the target group of users with maximal joint in?uential power, which has high impact on users’ buying, as is evident from the most re-cent ?ndings of marketing research (Katona et al. 2007, 2011).These marketing studies usually assume the condition of the in?u-ence spread (such as certain probability), and

based on these assumptions, their methods identify in?uential users to make as much in?uence spread as possible. But our method is not based on any assumption, and given the in?uence strengths between users, can be used with any cases. In addition, these existing stud-ies mainly involve the ‘‘binary value’’ applications, such as buying or not, or adopting or not, while our study encompasses additional‘‘continuous value’’ applications, such as reputation management,brand identi?cation, and public opinion guidance, which require changing users’ impressions of enterprises gradually. For these applications, discovering the group of users with maximal joint in?uential power is more important because their opinions can do the most to improve an enterprise’s image, strengthen brand recognition, and change public opinion.

2.3。传播的影响

最初提出这个问题，由佩德罗·多明戈斯和马特·理查德森（2001年多明戈斯和理查德森，理查德森和2002年多明戈斯），并遵循各种研究改进后，这项工作。这些研究的目的是探索的在线社交网络传播的影响力，并确定有影响的激活其他用户购买产品的用户。（2001年多明戈斯和理查德森），是用来模拟了一种基于马尔可夫随机场的传播影响力。在（即使Dar和2007年夏皮拉，肯普等人，2003年，肯普等，2005），传播过程中的影响力是使用线性阈值模型，独立的级联模型，和选民模型来描述。（al.2009本ZWI等，陈等人2009年，木村等人，2007），这个问题提出一些有效的近似算法。ENCE网络结构的影响进行了探讨（Galstyan等，2009）;产品购买下一个竞争激烈的社会网络分析（卡恩斯等，2007）。此外，其他的工作都集中在扩散SION营销研究和社会影响力。例如，这种方法被提出来识别特定的用户谁最影响ENCE别人的广告活动的目标和保留工作（特鲁索夫等，2010年），Nair等人。（2010）探讨影响社会交往和测量值有影响力的用户，在指导有针对性的销售收入最大化的营销策略研究（哈特兰等。2008）。

在这些作品中，我们的研究着重于发现最大的联合影响力，具有高影响用户的购买目标的用户群，是显而易见的，从最重百分之市场调研结果（卡托纳等2007 ，2011）。这些营销研究通常假设的影响基准蔓延的条件（如一定的概率），并根据这些假设，他们的方法确定有影响力的用户尽可能传播，使尽可能多的影响。但是，我们的方法还没有任何假设的基础上，给定的用户之间的影响强度，可用于任何情况下。此外，这些现有的研究主要涉及“二进制值”的应用程序，如购买或不采用或不，而我们的研究包括额外“连续值”的应用，如声誉管理，品牌识别和舆论引导，这需要逐步改变用户对企业的印象。对于这些应用，发现联合影响力最大的用户群，更重要的是因为他们的意见可以做的最来提高企业的形象，增强品牌知名度，改变舆论。

2.4. Community discovery

Much work has been done on community discovery in socialnetworks (Leskovec et al. 2010). The main purpose has been to partition the nodes of a network into groups, such that the

nodes n one group have better internal connectivity than external con-ectivity. Many proposed principles and algorithms regarding ommunity discovery have been classi?ed into several main cate-gories: spectral algorithms adopt the idea of principal components nalysis to discover communities (Kannan et al. 2004); network ow-based algorithms represent edges with pipes with unit capa-bility, and use max ?ow-min cut algorithms to identify communi-ties (Flake et al. 2003). Edge-counting ideas (Flake et al. 2000,Radicchi et al. 2004) take a set of nodes with more edges pointing nside the community than do the rest of the network, with some lgorithms using ‘‘betweenness centrality’’ to ?nd community oundaries. Recently, the modularity-based algorithms show otential performances which try to maximize the modularity of iscovered communities (Newman and Girvan 2004). Some studies nfer Web communities from link topology (Girvan and Newman 002); other work analyzes the community structure and semantic community (Gibson et al. 1998, Xu and Chen 2005). In addition, the characters of the social network community are explored, such as small-world property, power-law degree distribution, and network transitivity (Chen et al. 2008, Flake et al. 2002, Zhou et al. 2006). In contrast to these works, the main purpose of our study is to dis-cover a group of users with maximal joint in?uential power, rather than a group of users that is simply closely connected to eachother.

Our study is different from the existing ones in the following aspects. In contrast to existing studies that explore the importance of a single node in a social network, the objective of this study is to discover the target group of users with maximal joint in?uential power, which, according to the most recent ?ndings of marketing research (Katona et al. 2007, 2011), is a very important factor in?u-encing users’ adoption of products and their holding of positive sen-timental polarities about various companies on SNS. In addition,existing studies usually assume that social relationships between users are symmetric, and an undirected graph is used to model them. However, this is not true for some social relationships, such as the trust relationship. In this study, the directed graph is used to better model the asymmetric in?uence relationships.

2.4。社区发现

社区发现在socialnetworks（Leskovec等人，2010年），已经做了许多工作。的主要目的已分割成组的网络节点，例如，节点n个一组有较好的内部比外部con-ectivity的连通性。许多建议。社区发现的原理和算法被分为几个主要类别gories：光谱算法采用的想法的主要成分nalysis发现社区（Kannan等人，2004）;基于网络流算法代表边管单位能力性，并用最大流最小割算法识别通信（片状等，2003）。边缘计数想法（片状等，2000年，Radicchi等，2004年）一组节点与多个边缘指向内部通讯社区比其余的网络，一些lgorithms使用“中间中心”找到社区oundaries。近日，的模块化-基础的的的算法显示的otential的表演试试看哪个以最大限度地提高的模块化特性IsCovered该的社区（纽曼至2004年和格文）。一些的研究NFER链路拓扑（格文和纽曼002）的Web社区其他工作分析群落结构和语义社区（Gibson 等，1998年，徐和2005年陈）。此外，社交网络社区的字符进行了探索，如小世界，幂律分布，以及网络传递（陈等人，2008年，片状等，2002年，周某等人，2006）。在这些作品中，我们研究的主要目的是覆盖的用户群最大的联合影响力，而不是一个组的用户，简直是紧密相连的海誓山盟。

我们的研究是在以下几个方面与现有的不同。在现有的研究，探索在社交网络中的单个节点的重要性相比，本研究的目的是发现目标的用户群最大的联合影响力，其中，根据最新的市场调研结果（卡托纳等，2007年，2011年），是一个非常重要的因素，影响远隔千里的用户通过产品和各种SNS公司持有积极的孙中山timental的极性有关。此外，现有的研究通常假设用户之间的社会关系是对称的，是用来模拟一个无向图。然而，这是不正确的一定的社会关系，如信任关系。在本研究中，有向图来更好的模型的不对称的影响关系。

3. General process for discovering target groups

3.1. In?uence network

On SNS, the in?uence relationships exist only among some sers, and the in?uence strengths vary between different pairs of sers. In addition, opp osed to the friendship relationship, the in?u- nce relationship is asymmetric. Here, the in?uence network of sers is proposed to describe the in?uence relationships among sers on SNS represented as a directed graph. A simple in?uence etwork is shown in Fig. 1The in?uence network can be represented as G = (V, E, W), and includes the following components:

Node i: represents one user, such as ‘‘vemartin’’ and ‘‘Syntax’’ in ig. 1. The set of all nodes is marked as V = {1, . . . , i, . . . , n}.Arc (i, j): rep resents the in?uence relationship from user i to j.For example, the arc from ‘‘vemartin’’ to ‘‘Syntax’’ in Fig. 1 shows hat the user ‘‘vemartin’’ has in?uence on ‘‘Syntax.’’ The set of all arcs is marked as E = {(i, j) e V ? V|i – j}.Weight xij: Each arc is set a weight xij representing the strength of in?uence; for example, the in?uence strength from ‘‘vemartin’’ to ‘‘Syntax’’ is 1. The set of all weights is marked as W = {xij|(i, j) e E}. Cost cost(S): There are related costs for targeting a set of users,and the cost of targeting users in S is marked as cost(S).

3。发现目标群体的一般过程

3.1。影响网络

SNS的影响关系之间只存在一些SERS，优势各有不同，对不同的SERS的影响。此外，反对的友谊关系，影响NCE 关系是不对称的。在这里，影响网络的SERS SERS SNS上表示为一个有向图的影响之间的关系提出了描述。一个简单的影响ETWORK的图所示。网络（1）的影响可以表示为G =（V，E，W），并包括下列组件：

节点i：代表一个用户，如“vemartin”和“语法”中的IG。1。该组的所有节点被标记为V= {1，。。。i。。。，n}的圆弧（I，J）：表示从用户i的影响关系到j.For例如，产生的电弧，'' vemartin''''语法''图1显示了帽子的用户vemartin''''语法上的影响力。所有的弧集为E={（I，J）∈V/ V | I - J}重量XIJ标记：每条弧设置一个XIJ（重量）的强度影响，例如，从“vemartin的影响强度”的“语法”是1。所有的权重集被标记为W={XIJ|（I，J）E E}。成本（S）被标记为成本成本（S）：有用于定位的一组用户的相关成本，和S中的目标用户的成本。

In fact, the in?uence network can represent both directed and undirected in?uences, for the undirected in?uence, such as friend-ships, the two in?uence strengths, wvu and wuv, can be set with the same value.

事实上，影响网络可以代表定向和无向的影响，无向的影响，如朋友，这两个影响的优势，西弗吉尼亚和WUV，可以设置相同的值。

3.2. General process

As we know, there are many SNS, such as Myspace, Twitter, Epi-nions, and so forth. The proposed method can be used for discover-ing the in?uential groups based on data captured on SNS. Fig. 2 shows the general process of this method:

Data Collection. Some information about user pro?les and the in?uence relationships among users are collected from SNS. This information may include the following:

1) User pro?le in formation, such as user ID, user role, etc.

2) Social relationships among users, such as a friendship rela-tionship on Facebook and Myspace, a follower relationship on Twitter, and a trust relationship on Epinions. These social relationships usually indica te in?uence relationships among users as well, because users always more easily believe or accept the opinions of those with whom they have social relationships (Golbeck 2005, Lu et al. 2010, Massa and Avesani 2007).

3) Ratings on users’ reviews. In some S NS, users can rate the opinions of other users. For example, on the Epinions website, users can rate opinions at ?ve levels: ‘‘Not Helpful, Somewhat Helpful, Helpful, Very Helpful, Off Topic’’ to express their assessment of other users’ opinions. These rat ings also indicate the in?uence relationships among users to some degree: If user A always gives a high rating to user B’s reviews, user A tends to trust user B, and user B will very likely greatly in?uence user A.

4) Interaction information. On SNS, there are many interactions among users containing supporting or opposing informa- tion; mining these interactions using sentiment analysis and link-based technologies (Pang and Lee 2008) can iden-tify the consistent or inconsistent opinions between users to uncover the use r’s in?uence relationships.

3.2。一般过程

正如我们所知道的，有很多的SNS，如MySpace，Twitter的，EPI-nions，等等。该方法可用于发现SNS上捕获数据的基础上有影响力的群体。图图2示出了这种方法的一般过程：

数据收集。SNS的一些信息收集有关用户配置文件和用户之间的影响关系。此信息可能包括以下内容：

1）用户的个人资料信息，如用户ID，用户的作用，等等。

2）用户之间的社会关系，如友谊关系的关系在Facebook和Myspace，Twitter上的追随者关系，Epinions和信任关系。这些社会关系通常表明用户的影响之间的关系为好，因为用户总是更容易相信或接受那些与他们有社会的关系（Golbeck2005年，鲁等人，2010年，马萨和2007年Avesani的）的意见。

3）评级在用户的评论。在一些SNS，用户可以给其他用户的意见。Epinions网站，例如，用户可以率在五个级别的意见：“没有帮助的，有点帮助，帮助，非常有帮助的，题外话”来表达他们对其他用户的意见。这些收视率也表明使用者之间的关系，在一定程度上的影响：如果用户A总是给了很高的评价，以用户B的评测，用户à倾向于信任用户B，用户B很有可能会极大地影响用户A

4）交互信息。SNS上，还有有许多含有信息，支持或反对的用户之间的交互作用;开采这些相互作用利用情绪分析和基于链接的技术（2008年庞李）可以IDEN-TIFY用户之间的一致或不一致的意见，以揭示用户的影响之间的关系。

In?uence Network Construction. The in?uence network can be constructed by analyzing the collected data: The users compose the node set; the in?uence relationships are built by analyzing so-cial relationships, ratings, and interaction information. The in?u-ence strength is set according to the social relationship, the number of positive and negative ratings, and the number of sup-porting and opposing interactions among users. Here, let p be the number of positive ratings and supporting interactions from user v to u, and n be the number of negative ratings and opposing inter-epànTactions from v to u; thus, the in?uence strength is wuv ? 1àeepànT . (For1te different SNS, site-speci?c information can be explored to con-struct the in?uence network; two concrete cases are shown in the experimental evaluation section.)

Target Group Discovery. Based on the construct ed in?uence etwork, the target groups are discovered using the proposed models of mathematics programming. The method is presented in de-tail in the following section.

Results Display. Lastly, the in?uence network and discovered target groups are hown in a user-friendly way to support manag-ers’ quick decisions.

影响网络建设。影响网络可以通过分析所收集的数据构造：用户组成的节点集;关系建立的影响，通过分析社会关系，评分和交互信息。产生影响的强度是根据社会的关系，正面和负面评级的数量，以及数量燮移植和反对用户之间的互动。在这里，让p 是从用户v 到u 的积极评价和支持的互动，和n 是多少负面评价，，反对跨epànTactions 的从v 到u 的，因此，影响的强度是WUV?1àeepànT。 （For1te 不同的SNS 站点特定的信息可以探索的结构影响网络两个具体案件中所示实验评价部分。）

目标集团发现。构造影响ETWORK 的基础上，发现目标群体使用数学规划模型的建议。在下面的部分中去尾的方法。 结果显示。最后，影响网络和发现的目标群体是hown 一个用户友好的方式来支持管理ERS 快速的决定。

4. Computational models for discovering the most in?uential groups

Here, we assume that the users of the target group have bought products or hold positive opinions on products through some mar-keting strategies, and that these users can in?uence others’ buying decisions. Hence, the joint in?uential power of one group is de?ned as the sum of the in?uence streng ths of all users in this group on other users, without considering the inter-in?uence between them (also, the target group size is much smaller than the number of other users, and thus the inter-in?uence between them can be ig -nored) (Kempe et al. 2003, 2005). A number of models are pro-posed for discovering the target group with maximal joint in?uential power using mathematical programming technology.

4。计算模型发现最有影响力的群体

在这里，我们假设目标群体的用户已经购买了产品或产品持正面意见，通过一些营销策略，这些用户就可以影响其他人的购买决策。因此，定义为一组的联合影响力是此组中的所有用户对其他用户的影响强度的总和，不考虑它们之间的（也相互影响的情况下，目标组的大小的数量远小于其他用户，因此它们之间的相互影响可以ig-诺德）（肯普等人，2003，2005）。一些型号是亲合影发现目标群体的影响力最大联合使用数学编程技术。

4.1. Max-in?uence group problems

4.1.1. Basic Max-In?uence Group (Basic -MIG)

In the in?uence network, one target group corresponds to a sub -set of nodes, and the joint in?uential power of this subset corre -sponds to the sum of the weights on the arcs from the nodes of this subset to other nodes. Thus, discovering the target group with maximal joint in?uential power equals ?nding a subset of n odes S # V where the sum of the weights from the nodes in S to other nodes is maximal. That is:

.m a x .:i j i s j s w s t s v

∈∈?∑

here, S is the complementary set. This shows that although the number of users in S increases, the joint in?uential power may not monotonically increase, but even decrease. The reason is that the users in S may strongly in?uence only each other, not the users outside of the target group.

4.1。MAX-的影响力组的问题

4.1.1基本最大的影响集团（基本MIG ）

在受影响的网络中，一个目标组对应的节点的一个子集，这个子集的联合影响力对应于这个子集从节点到其他节点的弧上的权重的总和。因此，发现目标群体的联合影响力最大，等于发现节点S ＃V 其中S 中的点到其他节点的权重总和最大的一个子集。是：

.m a x .:i j i s j s w s t s v

∈∈?∑

这里，S 是补集。这表明，虽然在S 增加的用户数量的联合影响力可能并不单调增加，但甚至减少。其原因是，在S 的用户可能会强烈地影响只有对方，而不是用户的目标群体之外。

4.1.2. Certain Size Max-In?uence Group (CS -MIG)

As we know, the number of users of SNS is huge, and enterprisesonly have limited budgets for targeting customers; for this reason,discovering the target group with a certain group size that has maximal joint in?uential power is most desired for enterprises. This problem can be described as the following, with the group size less than or equal to t:

.m a x .:i j

i s j s w s t s v

s t ∈∈?≤∑

4.1.2。的一定规模最大影响集团（CS-MIG ）

正如我们所知道的，一些用户的SNS 是巨大的，和enterprisesonly 有针对客户的预算有限，因为这个原因，发现具有一定的群体规模，具有极大的影响力联合企业最需要的目标群体。这个问题可以描述为下面的内容，与该组的大小小于或等于t ：

.m a x .:i j

i s j s w s t s v

s t

∈∈?≤∑

4.1.3. Certain Cost Max-In?uence Group (CC -MIG)

In addition, the costs of targeting different users may be differ-ent. For example, if one user holds a negative sentiment polarity toward an enterprise, the enterprise may pay a higher cost to target this user through offering a big discount or use other ways.To consider this factor, the problem of discovering the target group with a certain targeting cost can be described as the following:

().m a x .:c o s i j

i s j s w s t s v

t s c ∈∈?≤∑

4.1.3一定的成本影响最大集团（CC-MIG ）

此外，针对不同用户的成本可能是不同的。例如，如果一个用户向企业持有负面情绪极性，企业可能会付出更高的成本，针对这个用户通过提供了很大的折扣或使用其他ways.To 的考虑这个因素，发现与目标群体的问题目标成本目标可

以描述如下：

().m a x .:c o s i j

i s j s w s t s v

t s c

∈∈?≤∑

4.2. Models

The above Basic-MIG , CS-MIG , and CC-MIG problems involve discovering a subset of nodes from a graph. Similar to the max-cut problem (Goemans and Williamson 1995), these are NP-hard problems. Recently, semide?nite programming (SDP) (Todd 2001)has proven to be an ef?cient way of partially solving this kind of problem (Goemans and Rendl 1999). SDP is a sub?eld of convex optimization concerned with the optimization of a linear objec-tive function over the intersection of the cone of positive semidef-inite matrices, and many practical problems in combinatorial optimization can be modeled or approximated as SDP problems.Similar with linear programming (LP), in the standard form of SDP, the objective function is the linear function of variable ma-trix (the inter product of constant matrix and variable matrix),and the constraints include both the linear equality constraints and positive semide?nite constraints on variable matrix. Follow-ing the method of the max-cut problem, the Basic-MIG , CS-MIG,and CC-MIG problems are formulated as integer programming models, which can be easily transformed into SDP and solved ef?ciently. Here, n + 1 decision variables x0, x1, . . ., xi, . . ., xn e {+1, à1} are de?ned; x0 is a reference variable, which denotes being in the target group S. If xi = x0, the node i is in S; otherwise, the node I is not in S. The Basic-MIG problem can then be formulated as follows:

()(){}00.:

1

m a x 14..:1,1,0,1,......,i j i j i j i j E i B a s ic M IG M o d e l w x x x x x x s t x i n

∈-+--∈-=∑

4.2。模型

上述的基本MIG ，CS-MIG 焊，和CC-MIG 问题的发现的曲线图中的节点的一个子集。类似的最大切的问题（Goemans 和威廉姆森1995），这些都是NP 难问题。近日，半定规划（SDP ）（2001年托德）已经被证明是一种有效的方式，部分地解决这种问题（1999年Goemans 的Rendl ）。 SDP 是Hermitian 矩阵的半正定矩阵锥的交点的线性目标函数的优化，可以模拟或近似为SDP problems.Similar 的线性组合优化在许多实际问题有关的凸优化的子场规划（LP ），SDP 的标准形式，目标函数变量的矩阵（产品间的常数矩阵变量矩阵）的线性函数，约束包括线性等式约束和半正定约束变量矩阵。后续ing 方法最大切问题，制定基本MIG ，CS-MIG ，CC-MIG 问题整数规划模型，可以很容易地转化为SDP ，并有效地解决。这里，n+1决策变量X0，X1，。 。 ，喜。 。 XN E {+1，A1}定义，x0是一个引用变量，它表示如果xi= X0，i 节点是在S;否则，节点我是不在S 中S 组在目标的基本MIG 问题的可以归结为如下：

()(){}00.1

m a x 14..:1,1,0,1,......,i j i j i j i j E i w x x x x x x s t x i n

∈+--∈-=∑

Note that if node i is in S and j is not, then xi = x0 – xj, and thus the corresponding part in the objective function is 1xij e1 t 1 à eà1T à eà1TT ? xij ; otherwise, if nodes i and j are both4 in the target group S, then xi = x0 = xj, and the corresponding part in the objective function in (1) is 1 xij e1 t 1 à 1 à 1T ? 0; if node i is4 not in S, and j is in S, then xi – x0 = xj, and the corresponding part is 1 wij e1 t eà1T à 1 à eà1TT ? 0; if node i is not in S, and j is not4 in S, and the corresponding part is 1 wij e1 t eà1T à eà1T à 1T ? 0.4 Thus, this model captures the joint in?uential power of nodes in S.

If the node i is in S, then x0xi = + 1; otherwise, x0xi = - 1. Thus,

Pn

i?1 x0 xi ? jSj à jSj ? jSj à en à jSjT ? 2jSj à n; here n is the number

à Pná

of all nodes, thus jSj ? 1i?1 x0 xi t n . Regarding the CS-MIG prob-2

lem, the size of the target group is less than or equal to t, that is,àPná16 t, and thus the CS-MIG problem is modeled asi?1 x0 xi t n2 follows:

()(){}00.0:

1

m a x 14..:1,1,0,1,......,2i j i j i j i j E i i i C S M IG M o d e l w x x x x x x s t x i n

x x t n

∈-+--∈-=≤-∑∑

请注意，如果S 中的结点i 和j 不，然后十一= X0 - 在xj ，在目标函数中的相应部分，从而是1xij D1t1àeà1T阑eà1TT?XIJ ，否则，如果节点i 和j 是both4，的在的目标S 组，然后XI= X0= XJ ，以及相应的目标函数中的一部分（1）1 XIJ D1t1帖撒罗尼迦前书 1 A= 0;如果节点i IS4 S 和j 是S ，则喜 - X0=在xj ，和相应的部分D1量wij1teà1T±1àeà1TT= 0，如果节点i 在S ，j 是在S 留学，相应的部分是D1量wijteà1Tàeà1T帖撒罗尼迦前书：0.4，因此，这个模型捕获节点的联合影响力在S

如果节点i 是在S ，则x0xi 的+ =1，否则，x0xi= - 1。因此，

PN

?X0 XI?àJSJ JSJ?JSJ 一个DNàjSjT?2jSj A N;这里n 是多少

阑PNA

所有节点，从而JSJ?1I= 1 X0 XI 第n 个。关于CS-MIG 问题2

LEM ，目标群体的大小是小于或等于T ，，àPná16吨，因此，CS-MIG 问题是仿照ASI= 1 X0第11届N2如下：

()(){}00.01

m a x 14..:1,1,0,1,......,2i j i j i j i j E i i i w x x x x x x s t x i n

x x t n

∈+--∈-=≤-∑∑

Let ci be the cost of targeting the node i. If the node i is in S, then x0xi = + 1, so the expression ci x0 x2t1 is equal to ci; otherwise,ci x0 x2t1 is equal to 0. Thus, the total cost of targeting the group Pni ci x0 x2t1 . Thus, the CC-MIG problem is modeled asS isi?1

()()

{}00.011:

1

m a x 14..:1,1,0,1,......,2i j i j i j i j E i n n

i i i

i i C S M IG M o d e l w x x x x x x s t x i n

c x x c c ∈==-+--∈-=≤-∑∑

∑

让CI 是针对节点i 的成本。如果结点i 和S 中，然后x0xi=+1，所以词x0的x2t1的表达是等于词，否则，词X0x2t1等于0。因此，总成本针对组PNI 词X0x2t1的。因此，CC-MIG 问题建模屁股ISI= 1

()(){}00.011:

1

m a x 14..:1,1,0,1,......,2i j i j i j i j E i n n

i i i

i i C S M IG M o d e l w x x x x x x s t x i n

c x x c c ∈==-+--∈-=≤-∑∑

∑

In these three models, both the objective function and the con-straints are linear in xixj, and they can thus be easily relaxed as SDP problems. Let Y = xxT, and the three models can be relaxed as the following SDP for ef ?cient solution (Goemans and Rendl 1999;Goemans and Williamson 1995):

()()

()()()0.00,01

2

11R e :

1

m a x 14..:1,0,1,......,0

R e 1

m a x 14..:1,0,.....,220

i j i o j i j i j E ii ij i j ij i j E ii n

i i n n

ij i j B a s ic M IG la x a tio n w Y Y Y s t Y i n

Y C S M IG la x a tio n

w Y Y Y s t Y i n

Y t n Y t n Y ∈?===-+-==≥-+-==≤-≤-≥∑∑∑

∑∑

在这三种模式中，目标函数的关系是线性在xixj ，因此，他们可以很容易地放松SDP 问题。让Y= XXT ，可以轻松高效的解决方案（Goemans 和的Rendl1999 Goemans 和威廉姆森，1995）以下的SDP 的三种模式：

()()

()()()0.00,01

2

11R e :

1

m a x 14..:1,0,1,......,0

R e 1

m a x 14..:1,0,.....,220

i j i o j i j i j E ii ij i j ij i j E ii n

i i n n

ij i j B a s ic M IG la x a tio n w Y Y Y s t Y i n

Y C S M IG la x a tio n

w Y Y Y s t Y i n

Y t n Y t n Y ∈?===-+-==≥-+-==≤-≤-≥∑∑∑

∑∑

Pn PnPn2The constrainti?1j?1 ci c j Y ij 6 e2C ài?1 ci T is similar way to the one in CS-MIG Relaxation.

After ?nding the solutions to these SDP problems, the approx -imate solutions of the

Basic-MIG, CS-MIG, and CC-MIG problems can be determined through the randomized rounding procedure (Goemans and Williamson 1995): Compute the Cholesky factor-ization of the SDP solution and take the columns of Cholesky fac-torization as the vectors vi (i = 0, . . .n) corresponding to the nodes I (i = 0, . . ., n), choose a random hyperplane through the origin (the random vector is generated with the normal distribution with mean 0 and variance 1) and partition the vectors vi (i = 0, . . ., n).If vi (i = 1, ..., n) falls on the same side as vector v0, the decision variable xi takes the value of 1; otherwise, it is à1. For the CS-MIG and CC-MIG problems, additional processes are executed tomake sure the target groups satisfy the size and cost constraints:

If the number of nodes in the current target set is greater than t (or the cost of targeting the current group is large than C), remove the variable which has the smallest sum of the in?uence weights on the nodes out of the target set. Repeat the process until the size of the target set is less than t (or the cost of targeting the cur-rent group is less than C). The computing cost of the algorithm comes mainly from solving the SDP model, which requires p???Oen lne1=eTTsteps (Todd 2001). This randomized rounding algorithm can lead to a 0.79607 times the optimum value of the original problem.

PN PnPn2The constrainti?1J= 1 CI CJ?IJ6 D2C AI= 1 CIT是CS-MIG放松的一个类似的方式。

这些SDP问题找到解决方案后，基本MIG，CS-MIG，和CC-MIG问题的近似解可以决定通过随机的四舍五入程序（1995年Goemans和威廉姆森）：计算的Cholesky因子化的SDP解决方案，并采取作为的Cholesky因子torization 的列向量vi的（= 0，... n）的（I=0，...，n）时，通过随机选择一个超平面的节点对应于原点（产生均值为0，方差为1的正态分布的随机向量）和分区的向量vi的（= 0，...，n）的，如果vi（= 1，...，n）的下降的决定变量xi0作为载体的同一侧，以值为1，否则，它是1处。对于CS-MIG和CC-MIG问题，附加进程的执行tomake确定的目标群体满足的尺寸和费用的限制：

如果在当前的目标设定的节点的数目大于吨（或针对当前组的成本比C大），则删除该变量的节点上的设定目标具有最小的影响的权重的总和。重复该过程，直到设定目标的大小是小于吨（或目标电流租金组的成本比C少）。该算法的计算成本主要来源于解决SDP模式，要求pffiffiffi OD的?LND1=eTT步骤（托德·2001年）。这种随机化的舍入算法可以导致一个0.79607倍于原问题的最佳值。

4.3. Indirect in?uence

In addition, indirect social in?uence also plays a very important role in people’s decision making (Denrell 2008, Forgas and Wil-liams 2001). On SNS, users are indirectly in?uenced by their friends’ friends. Our method considers the indirect in?uence in the following way: The weight set W in the models is updated as: W ? W t k á W 2 ; here, W2 represents the indirect in?uence through one medium node, and k is the ratio of indirect in?uence in the ?nal weight set W. Similarly, the higher-order indirect in?u-ence can be considered in this way, although it rarely occurs in reality (Forgas and Williams 2001, Nair et al. 2004).

类别修订的聚类系数

书籍

电影

音乐

儿童与家庭

家居与园艺

电子

电脑硬件

体育和户外运动

汽车及摩托车

计算机软件 9535 249 7353

221 6131 231 6316

272

5383 210 2722 258 2649

168 1805 197 1701 210

1386 263

4.3。间接影响 此外，间接的社会影响力也起着非常重要的作用，在人们的决策（2008年Denrell Forgas2001年WIL-liams 的）。 SNS 上，用户通过朋友的朋友的间接影响。我们的方法考虑了间接的影响，以下列方式：更新模型中的权重集合W 如下：W?WtK A W 2，在这里，W2表示间接的影响，通过一个介质节点，k 是比例的间接集W 的最终重量的影响力，同样地，更高阶的间接影响ENCE 可以考虑以这种方式，虽然它在现实中很少发生（2001年Forgas 和Williams ，Nair 等人，2004）。

5. Experimental evaluation

In order to evaluate the effectiveness of the proposed methods,two experimental evaluations using two real datasets were con-ducted: The ?rst evaluation adopts the dataset from the Epinions website, and the proposed Basic-MIG, CS-MIG , and CC-MIG models are compared with two benchmark methods; the second evalua-tion adopts the dataset from the Twitter website, and the perfor-mance of the proposed models is evaluated based on the large-scale dataset with sparse

in?uence relationships.

5.1. Experiment evaluation I

5.1.1. Epinions dataset

The dataset used in this evaluation is from the popular Epinions website, which is a user opinions website supporting social networking functions. On this website, users can rate products and express their opinions, thereby building trust relationships with others by adding them to their trust lists, and blocking those users whose comments they do not trust or do not wish to read. The system shows the trusted users’ opinions at the top of the list,and thus it can be assumed that users are in?uenced most by this group. For each product category, the website provides a ranking list of the top 1000 users according to the total hits to member re-views. In this evaluation, information about users from the ranking lists of ten different product categories (listed in Table 1) is ex-tracted, including their rankings, as well as the trust relationships among them, and so forth.

5.1.1.1. Constructing the in?uence network. For the extracted data in each product category, one in?uence network is built: 1000 users comprise the node set. If user i is trusted by user j, there exists an in?uence relationship from i to j; here, the in?uence strength is set as 1. A summary of characteristics of the 10 in?uence net-works from different categories is shown in Table 1, which displays obvious differences in in?uence relationship density and weighted degrees of nodes. For example, the in?uence network of the Books category has the densest in?uence relationships: On average, each node has 32.5 in?uence relationships, 28 nodes have more than150 weighted degrees, and most nodes have more than 10 weighted degrees. In contrast, the in?uence network of the Com-puter Software category has relatively sparse in?uence relation-ships, on average, each node having only 4.7 in?uence relation-ships, and 589 nodes having zero out-degrees.

5.1.2. Experimental settings

Since discovering that the target group with joint in?uential power is an NP-hard problem and there are no available bench-mark datasets, it is infeasible to evaluate the proposed method by comparing the d iscovered target groups with the ‘‘Ground Truth’’ groups. Here, we adopt a similar approach to that of other studies (Kempe et al. 2003, Richardson and Domingos 2002) on the in?uence of social networking: Metrics are de?ned, and the proposed method is compared with other benchmark methods based on the metrics. In this evaluation, the joint in?uential power of the discovered target group (the sum of the in?uence strengths of all users of this group on other users), is used as the metric, and two benchmark methods, the weighted-degree centrality method and the revised cluster coef?cient method (Zhang et al. 2008),are used to compare with the proposed method.

Weighted-degree centrality method. This is a commonly used method for measuring the importance and in?uence of nodes in a network (Barrat et al. 2004, Newman 2004, Opsahl et al. 2008), and some studies (Kate et al. xxxx, Wan and Tian 2010, Zhu et al. 2008) have adopted this method for measuring the in?uence of nodes in social networking analysis. Here, the weighted-degree centrality of each user is calculated as the sum of the in?uence strengths of this

user on others, the users are ranked according to their weighted-degree centralities, and the target group is chosen based on this ranking list: For the Basic-MIG problem, the top users are sequen-tially put into a group until the group reaches a maximal in?uential power; for the CS-MIG problem, the top t users comprise the target group. Revised cluster coef?cient method. The original method (Zhang et al. 2008) uses the number of written reviews and the trust relationships to discover the target group. Here, we adapt this method to the in?uence network: First, users are ranked according to the number of their written reviews. Then the users and their relationships are orderly added to the target group, and the clustering coef?cient of the target group is calculated. The adding process is stopped when the clustering coef?cient is less than the threshold. For the basic MIG problem, the clustering coef?cient t hreshold is gradually reduced until the target group achieves the maximal in?uential power. For the CS-MIG problem, the clustering coef?cient is set to make the target group reach a certain size.

For the Basic-MIG and CS-MIG problems, the respective models are used to discover the target groups, and the joint in?uential powers of the discovered target groups are compared. To evaluate the performance of the CC-MIG model, the ratings of users for brand A are extracted, which are scaled from 1 to 5 (1 being the most negative polarity, and 5 the most positive). The costs of tar-geting users are set to be proportional to their sentiment polari-ties: Let si be the sentiment polarity of user i, then the cost of targeting user i is set as ci ? sci (here, c is a constant cost with a value of 5). If the user holds negative sentiment polarity, the cost of targeting him or her is high; otherwise it is low. To consider the cost factor, the two benchmark methods are revised as follows: In the weighted-degree centrality method, the top users in the rank-ing list are sequentially put into the group until the sum of the cost of the target group exceeds the budget constraint C; in the re-vised cluster coef?cient method, the clustering coef?cient is set to ensure that the cost of the target group does not exceed the budget constraint C. The CC-MIG model and the two benchmark methods are then compared. In this experiment, the DSDP MA T- LAB toolbox (DSDP 2006) is used to solve the relaxed SDP problems.

。5。实验评价

为了评估所提出的方法的有效性，两个实验的评价都是使用两个真实数据集进行：第一次评估采用的数据集从Epinions 网站，建议基本MIG，CS-MIG，CC-MIG模型与两个基准方法相比，第二次评估采用的数据集从Twitter的网站，提出的模型性能评估的基础上的大型数据集的稀疏的影响关系。

5.1。实验评价我

5.1.1。Epinions数据集

本评价中使用的数据集是从流行Epinions网站，这是一个用户的意见支持社交网络功能的网站。在这个网站上，用户可以在利率产品，并表达他们的意见，从而与他人建立信任关系，通过将它们添加到信任列表，并阻止那些他们不信任或不希望阅读的用户评论。系统显示的受信任的用户的意见，在列表的顶部，因此它可以假定用户的影响这一组。对于每一个产品类别，该网站提供了一个排行榜的前1000个用户的总命中成员意见。在该评价中，从10个不同的产品类别（列于表1）的排序的列表的有关用户的信息提取，包括自己的排名，以及它们之间的信任关系，等等。

5.1.1.1。影响网络的构建。对于各产品类别中的提取数据，一个影响网络的建立：1000个用户，包括节点集。如果用户i的用户j的信任，存在从i到j的影响关系，在这里，影响强度设置为1。10影响从不同类别的网络工程的概要的特性示于表1中，其中显示了明显的差异，影响的关系密度和节点的加权度。例如，影响网络的书籍类具有影响最密集的关系：平均而言，每个节点有32.5影响的关系，28个节点，有超过150加权度，大多数节点有10个以上的加权度。相比之下，影响网络的电脑软体类别有关系，平均而言，每个节点具有影响关系只有4.7船舶，和589个节点，具有零出度相对稀疏的影响。

5.1.2实验设置