Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina A Constrained Multi-view Clustering Approach to Influence Role Detection Chengyao Chen1, Dehong Gao2, Wenjie Li1, Yuexian Hou3 1 Department of Computing, The Hong Kong Polytechnic University, Hong Kong 2 1688cn, Alibaba.INC(Hangzhou), China 3 School of Computer Science and Technology, Tianjin University, China cscchen@comp.polyu.edu.hk, dehong.gdh@alibaba-inc.com, cswjli@comp.polyu.edu.hk, yxhou@tju.edu.cn Abstract others the latest news of a product. And someone promotes the product by popularity. It is quite clear that different Twitter has provided people with an effective way to communicate and interact with each other. It is an influential users play different influence roles. Meanwhile, a undisputable fact that people’s influence plays an company may have different objectives in different important role in disseminating information over the promotion stages and needs users with different influence Twitter social network. Although a number of roles to conform to [Brown and Hayes, 2008]. For example, research work on finding influential users have been a company which targets to improve product brand awareness reported in the literature, they never really seek to may want to choose the users with high popularity to help distinguish and analyze different influence roles, with. However, for a company whose product quality is which are of great value for various marketing questioned by customers, it may be a better choice to invite purposes. In this paper, we move a step forward to domain experts who have professional knowledge to explain further detect five recognized influence roles of and convince. Selecting influential users with appropriate Twitter users with regard to a particular topic. By influence roles in accordance with specific marketing exploring three views of features related to topic, objectives is more effective than just seeking for the most sentiment and popularity respectively, we propose a influential ones in general. novel constrained multi-view influence role Despite the importance of influence role, previous work clustering approach to group potential influential mostly emphasizes on measuring the general influence power Twitter users into five categories. Experimental of a user on others through the information of the netwrok results demonstrate the effectiveness of the structure[Cha et al., 2010; Weng et al., 2010], or maximizing proposed approach. the influence propagation which assists companies to find the proper set of people to promote products [Kempe et al., 2003; 1 Introduction Chen et al., 2009]. Without any exception, they all take the Nowadays, Twitter has become one of the most popular influence as the same type. The lack of considering the effects social media platforms for people to share information and of different influence roles on different marketing objectives communicate with each other. It creates more and more new will inevitably hinder the companies from proposing more business opportunities with a variety of online marketing suitable marketing strategies. This motivates us to further activities [Anagnostopoulos et al., 2008]. Recent years have analyze and detect different influence roles of users, which witnessed that an increasing number of enterprises have could be used to further extend the previous work in started to attach importance to locating favorable influential achieving different marketing goals. [Chen et al., 2014] users and manipulating their opinions to attract potential proposed the idea to distinguish different types of influential customers or improve sales. Understanding social influence users, but lacked compelte study on how to detect them. over large-scale networks is crucial to business marketing Table 1. Five categories of influence role. management. Role Category Influence Manner Marketing Effect Although all influential users perform influence on others, Support and defend Enthusiast Improve sales [Brown and Hayes, 2008]has verified that the way people use products to influence others varies and produces different effect. Information Publish product Enhance brand Someone always strongly praises a product and persuades Disseminator information memorability others to buy. Someone changes others’ opinions on a Gather facts and Improve Expert professional opinions reputation product with professional analysis. Someone timely informs Improve Copyright © 2015 for the individual papers by the papers' authors. Celebrity Popular among people awareness Copying permitted for private and academic purposes. This Show no obvious volume is published and copyrighted by its editors Others None influence 29 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina To better characterize influence roles, we define five the mutual information, the K most relevant words that co- distinct categories with reference to the definition in the occur with the topical word within a window of size two are WOMMA’s influencer guidebook extracted as keywords to form the topic profile collectively. (www.womma.org/influencers). They are enthusiast, These K words provide a more complete picture of the topic information disseminator, expert, celebrity and others. The than the topical word itself. For all the tweets of a given user, brief descriptions of them are summarized in Table 1. We can a topical vector weighed by tf-idf is built to capture his/her clearly see that one’s influence role is largely determined by word distribution over the extracted keywords. his/her behaviors and personal characteristics, but not totally Sentiment-view Representation dependent on how much influence he/she has. Different from The sentiment view reveals the preferred attitudes when a previous work that measures users’ influence mainly based user expresses his/her opinions and tends to differentiate on social connections, we summarize three aspects that help among the enthusiast who often posts tweets with positive to distinguish influence roles, including the interest to a topic sentiments, the disseminator whose tweets is mainly neutral (e.g., enthusiast, information disseminator and expert pay ones and the expert whose opinions may be either positive or more attention than the other two), the attitude to the topic negative. To measure the sentiment of users, the lexicon (e.g., enthusiast always praises, expert sometimes praises and AFINN (http://www2.compute.dtu.dk/~faan/data/) is used, sometimes not) and the popularity over the social network where each word is attached with an integer value between (e.g., celebrity has more followers). Accordingly we extract negative five and positive five, denoting its sentiment polarity three views of features, i.e., the topic view, the sentiment and strength. Based on this lexicon, the positive/negative view and the popularity view from users’ posts and profiles sentiment scores of a tweet are calculated by aggregating the for influence role detection. sentiment strengths of all the positive/negative words it We also note that each view can only partially reflect the contains. The sentiment view representation of a user is then influence role from its own perspective. However, when they defined as the average positive-sentiment score and average complement with each other, the three views together provide negative-sentiment score of all his/her tweets more complete information for influence roles. Based on the three-view user representations, we propose a novel Popularity-view Representation Constrained Multi-view Influence Role Clustering (CMIRC) Apart from the interests and attitudes to a topic, the popularity approach upon an optimization framework to partition (or to say the authority) of a user can also imply the influence influential users into five recognized categories. Unlike other role in some extent. Three features are selected including the existing multi-view clustering approaches, CMIRC allows number of followers, the number of followees and a binary the cluster numbers in the different views to be different and value indicating whether a user account is verified or not. The so provides more flexibility for integrating data from multi- popularity view tends to distinguish the people with different views. It connects the local clustering information from each levels of popularity like celebrities and enthusiasts. individual view and the global multi-view clustering results with a local-global mapping mechanism. 2.2 Constrained Multi-view Influence Role Another advantage of CMIRC is its capability to Clustering incorporate the prior knowledge based upon the semi- To better use the data collected from multiple sources, multi- supervised learning framework. Actually, it is very common view clustering approaches partition data into clusters by that the influence roles are known to a small number of users integrating features from multiple views. They have been who are easily identified by a company. Then people can use successfully applied to image recognition and text mining, etc. such information as the prior knowledge to find out many [Bickel et al., 2004; Cai et al., 2013; Liu et al., 2013]. These others for their needs. To incorporate the prior knowledge to approaches share a common assumption, i.e., the features guide clustering, we apply two kinds of group-level from each single view are complete for clustering, yet better constraints, the same-cluster constraints and the different- clustering performance can be expected by exploring the rich cluster constraints, to define which groups of users must be information among multiple views. Naturally, the cluster or must not be in the same cluster. The experimental results numbers of different views are often supposed equal to the demonstrate the effectiveness of CMIRC when compared final multi-view cluster number. From the previous analysis, with other single-view and multi-view clustering approaches however, we believe that it is more reasonable and practical to allow the cluster numbers of different views to be different 2 Influence Role Detection for influence role detection. As a result the clustering results in each view will be also different from the ultimate 2.1 Three-View User Representation clustering results. To this end, we develop a Constrained Topic-view Representation Multi-view Influence Role Clustering (CMIRC) approach to The motivation of using topic view is the intuition that group data into different numbers of clusters in individual different roles may have different degrees and different views (i.e., local clusters) and utilize the mapping matrix to focuses of attention to the topic. To start with, a word like bridge the gap between the single-view clusters and the multi- “iPhone” is selected as the topical word. Then, measured by 30 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina view clusters (i.e., global clusters). The introduction of the Figure 1 explains how 𝑢𝑖 ’s local cluster in view j mapping matrix is one of the main contributions of this work. corresponds his global cluster. Assume that 𝑢𝑖 belongs to the Another advantage of this approach is its semi-supervised first global cluster as presented in 𝐺𝑖 and the mapping matrix framework that allows us to incorporate the prior knowledge describes the first global cluster is mapped to the second local easily. Say, we can take a small number of users whose cluster. Then 𝑢𝑖 should be found in the second local cluster. influence roles are manually labeled as the prior knowledge Apart from the use of mapping matrix, two types of to guide the clustering of others. To incorporate the prior constraints are also integrated into CMIRC. They are defined knowledge into CMIRC, we employ two kinds of group-level through user groups 𝑢𝑔𝑖 = {𝑢1 , 𝑢2 , … , 𝑢𝑛(𝑢𝑔𝑖) } , where constraints [Law et al., 2004] to define which group of users 𝑛(𝑢𝑔𝑖 ) is the number of users in this user group 𝑢𝑔𝑖 . Same- must be or must not be in the same cluster. Specifically, the Cluster constraints are a set of user groups, i.e., 𝑆𝐶 = same-cluster (𝑆𝐶) constraints include several groups of users {𝑢𝑔1 , 𝑢𝑔2 , … , 𝑢𝑔𝑙 } . The users in each 𝑆𝐶 group must be and the users in each group must belong to the same cluster, assigned to the same cluster. Different-Cluster constraints are either local or global cluster. The different-cluster ( 𝐷𝐶 ) a set of user group pairs, i.e., 𝐷𝐶 = {𝑝1 , 𝑝2 , … , 𝑝𝑟 } and 𝑝𝑘 = constraints contain several group pairs and the users in the ⟨ 𝑢𝑔𝑖 , 𝑢𝑔𝑗 ⟩. The users in two different groups of a pair in 𝐷𝐶 two groups of a pair cannot be in the same cluster. To better describe our approach, let’s start with a variant must belong to different clusters. All users in 𝑆𝐶 and 𝐷𝐶 K-means clustering algorithm which utilizes data from compose 𝑈𝑐𝑜𝑛 . Compared with the pair-wise constraints, multiple sources [Cai et al., 2013]. Let 𝑈 = {𝑢1 , 𝑢2 , … , 𝑢𝑛 } during cluster assignment, we could assign a cluster to the represents n Twitter users. Each user 𝑢𝑖 is represented by m whole group without the need to assign users to clusters one views of features, 𝑋𝑖 = {𝑋𝑖1 , 𝑋𝑖2 , … , 𝑋𝑖𝑚 } , where the j-th by one. Such a strategy avoids computational complexity in 𝑗 the optimization procedures introduced later. element 𝑋𝑖 represents the features of view j, and it is a row Finally, CMIRC that partitions the users 𝑈 into t clusters with vector containing 𝑑𝑗 elements. Then a typical multi-view m-view features constrained by 𝑆𝐶 and 𝐷𝐶 can be clustering task can be formulated as the following formulated by the following optimization problem optimization problem. 𝑚 𝑛 𝑚 𝑛 𝑇 𝑗 𝑗 𝑇 min ∑ ∑ 𝛼𝑗 ‖𝑋𝑖 − 𝐺𝑖 𝑀 𝑗 𝐶 𝑗 ‖ (1) min ∑ ∑ 𝛼𝑗 ‖𝑋𝑖 − 𝑃𝑖𝑗 𝐶𝑗 ‖ 𝐺,𝑀,𝐶 2 𝑃,𝐶 2 𝑗=1 𝑖=1 𝑗=1 𝑖=1 𝑡 𝑚 𝐾𝑗 𝑚 𝑠. 𝑡. ∑ 𝑃𝑖𝑗𝑘 = 1, 𝑃𝑖𝑗𝑘 ∈ {0,1}, ∀𝑖 = 1,2, … , 𝑛, ∑ 𝛼𝑗 = 1 𝑠. 𝑡. ∑ 𝐺𝑖𝑘 = 1, 𝐺𝑖𝑘 ∈ {0,1}, ∑ 𝛼𝑗 = 1, 𝑘=1 𝑗=1 𝑘=1 𝑗=1 𝐾𝑗 𝑡 1×𝐾 𝑗 Similar to K-means, 𝑃𝑖𝑗 ∈ here describes the cluster 𝑗 𝑗 indicator for user 𝑢𝑖 in view j. It also represents the local ∑ 𝑀𝑖𝑘 ≥ 1, ∀𝑖 = 1, … , 𝑡, ∑ 𝑀𝑖𝑘 = 1, ∀𝑘 = 1, … , 𝐾𝑗 , 𝑗 𝑗 𝑘=1 𝑖=1 clustering results. 𝐾𝑗 and 𝐶 𝑗 ∈ 𝑑 ×𝐾 denote the cluster 𝑗 𝑀𝑖𝑘 ∈ {0,1}, ∀𝑢𝑖 , 𝑢𝑗 ∈ 𝑢𝑔𝑘 ∧ 𝑢𝑖 ≠ 𝑢𝑗, 𝐺𝑖 = 𝐺𝑗 , number and cluster centers in view j. 𝛼𝑗 is a factor to balance the weight of view j. If the cluster numbers in all m views are ∀⟨𝑢𝑔𝑞 , 𝑢𝑔𝑝 ⟩ ∈ 𝐷𝐶 ∧ ∀𝑢𝑖 ∈ 𝑢𝑔𝑞 ∧ ∀𝑢𝑗 ∈ 𝑢𝑔𝑝 , 𝐺𝑖 ≠ 𝐺𝑗 the same (i.e., 𝐾𝑗 =t, where t represents global cluster where 𝐺𝑖 represents the global cluster assignment for user number), 𝑃𝑖𝑗 for all the views should be consistent. This 𝑢𝑖 which satisfies 1-of-K coding scheme. 𝐶 𝑗 is the local implies that the local clustering results in every view are cluster center in the j-th view and 𝑀 𝑗 is the mapping matrix. equal to the global clustering results. However, with our 𝑀 𝑗 satisfies the constraints that every local cluster must be assumption, the cluster number in each view is different, so mapped to at least one global cluster and every global cluster we cannot derive the global clustering results directly from must be mapped to one and only one local cluster. 𝑃𝑖𝑗 . In order to connect local clustering and global clustering In order to solve this optimization problem, we rewrite the together, we transform the local clustering results 𝑃𝑖𝑗 in view objective function in Equation (1) as Equation (2), and apply j into the combination of global cluster assignment 𝐺𝑖 ∈ 1×𝑡 the following iterative updating process to solve it. 𝑚 𝑗 and a mapping matrix 𝑀 𝑗 ∈ 𝑡×𝐾 . 𝑂 = min ∑ 𝛼𝑗 𝐻 𝑗 , (2) 𝐺,𝑀,𝐶 Figure 1. Illustration of global and local cluster mapping 𝑗=1 𝑇 𝑗 𝑗𝑇 𝑇 𝑇 where 𝐻 𝑗 = 𝑇𝑟{(𝑋𝑗 − 𝐶 𝑀 𝐺 𝑇 )𝐷 𝑗 (𝑋𝑗 − 𝐶 𝑗 𝑀 𝑗 𝐺 𝑇 )𝑇 , and 𝐷 𝑗 is the degree matrix derived from 𝐸 𝑗 . 𝑗 1 𝑇 × t = 𝑑𝑖𝑖 = 𝑗𝑖 , ∀𝑖 = 1,2, … 𝑛, and 𝐸 𝑗 = 𝑋𝑗 − 𝐺𝑀 𝑗 𝐶 𝑗 (3) 2‖𝑒 ‖ t 𝐾𝑗  Fix 𝐺, 𝑀 𝑗 , 𝐷 𝑗 and update local cluster center 𝐶𝑗 As stated before, the combination of 𝐺𝑖 and 𝑀 𝑗 represent 𝐾𝑗 local cluster results. In this step, the local cluster centers are Global cluster 𝑮𝒊 Mapping matrix 𝑴𝒋 Local cluster 𝑷𝒊𝒋 31 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina updated by minimizing the distances from users to their are constrained by Same-Cluster as the influence roles of corresponding clusters. It is solved by differentiating the these clusters. objective function in Equation (2) for each view with respect to 𝐶 𝑗 . The optimal solution of 𝐶 𝑗 is obtained by setting the 3 Experiments and Discussion derivation to zero, which gives us Four topics about well-known electronic products, “iPhone”, 𝑇 𝑇 𝐶 𝑗 = 𝛼𝑗 𝑋𝑗 𝐷 𝑗 𝐺 𝑗 𝑀 𝑗 (𝛼𝑗 𝑀 𝑗 𝐺 𝑇 𝐷 𝑗 𝐺𝑀 𝑗 )−1 (4) “Samsung Galaxy”, “Xbox” and “PlayStation” are selected  Fix 𝑀 𝑗 , 𝐶 𝑗 , 𝐷 𝑗 and update global cluster assignment 𝐺 to construct the experimental datasets. We collect the tweets We update 𝐺 through each row of its, 𝐺𝑖 in the following that contain the topical word like “iPhone” from 3rd to 30th order. First we update 𝐺𝑖 for the users who are not April 2014. Among users who post these tweets, the ones who have more than 500 followers and have been re-tweeted constrained separately, and then update 𝐺𝑖 for the users who at least once are regarded as influential users. The size of an are in 𝑈𝑐𝑜𝑛 together. In particular, if the user 𝑢𝑖 is not influential user pool ranges from 4912 (for Samsung Galaxy) constrained, we locate the local cluster for each user through to 90906 (for iPhone). To be consistent, 4912 influential users the mapping matrix. Then, what we need to do is to find are sampled for each topic. These users together with their 𝐺𝑖 from its limited solutions that minimize the sum of tweets and account information are used in the experiments. distances between it and the center of its assigned local Due to the lack of annotated datasets, for each topic we cluster for each view, as presented in the Equation (5). randomly select 200 from 4912 influential users and invite 𝑚 𝑗 𝑇 human annotators to label their influence roles for evaluation 𝐺𝑖 = argmin ∑ 𝛼𝑗 ‖𝑋𝑖 − 𝐺𝑖 𝑀 𝑗 𝐶 𝑗 ‖ (5) purpose by providing users’ posts and their account 𝐺𝑖 2 𝑗=1 information. The numbers of the annotated users across five Constrained by 𝑆𝐶 and 𝐷𝐶 , we give each user group in influence roles are presented in Table 2. We randomly choose 𝑈𝑐𝑜𝑛 a global cluster assignment, i.e., 𝐺𝑐𝑜𝑛(𝑢𝑔𝑖 ) , a row vector 1/5 users of each influence role to build the constraints that represents the assignment for users in user group 𝑢𝑔𝑖 in required by CMIRC, and the rest are used for evaluation. 𝑆𝐶. By concatenating the assignment vectors for each user Table 2. Evaluation data on four topics group, we form a certain number of candidate assignment Role Information Enthusiast Expert Celebrity Others matrixes that guarantee the 𝐷𝐶 constraints in column. From Topic Disseminator all these candidates, the one that minimizes the objective iPhone 9 31 13 20 127 Galaxy 21 32 15 19 113 function in Equation (6) is defined as 𝐺𝑐𝑜𝑛 , Xbox 20 25 14 15 126 𝑛(𝑢𝑔 ) 𝑗 𝑇 𝑇 𝐺𝑐𝑜𝑛 = argmin ∑𝑚 𝑙 𝑗 𝑗 𝑗=1 ∑𝑖=1 ∑𝑘=1 ‖𝑋𝑢𝑔𝑖𝑘 − 𝐺𝑐𝑜𝑛(𝑢𝑔𝑖 ) 𝑀 𝐶 ‖ 𝑖 PlayStation 13 29 15 14 129 𝐺𝑐𝑜𝑛 2 (6) We compare CMIRC with (1) Baseline K-means 𝑗 where 𝑋𝑢𝑔𝑖𝑘 are the j-view features of user 𝑢𝑘 who is in clustering (BKC) and Constrained K-means clustering (CKC) group 𝑢𝑔𝑖 . Then the global cluster assignment 𝐺𝑘 for user that concatenates three views together; (2) two existing multi- 𝑢𝑘 in user group 𝑢𝑔𝑖 is regarded as 𝐺𝑐𝑜𝑛(𝑢𝑔𝑖) . view clustering approaches, i.e., Multi-view K-means Clustering (MKC) [Cai et al., 2013] and Negative Matrix  Fix 𝐺, 𝐶 𝑗 , 𝐷 𝑗 a, and update global and local cluster Factorization (NMF) based Multi-view Clustering (NMFMC) mapping matrix 𝑀 𝑗 [Liu et al., 2013]. To further understand the contribution of 𝑗 𝑀 is the mapping matrix between global and local clusters. each view, we also compare with (3) Constrained Single- For each view, based on the constraints for 𝑀 𝑗 , we construct View K-means Clustering (CSCtopic, CSCsentiment and CSCaccount) candidate mapping matrixes and possible choices for the and (4) Constrained Two-View K-means Clustering local cluster assignment by transforming from the global (CMIRCts, CMIRCsa and CMIRCta). In addition, (5) CMIRC cluster assignment 𝐺. The one that assigns users to the best without constrains (MIRC) is also compared. Three local clusters to guarantee the overall minimized distance commonly-used metrics are used to evaluate performances. over all the users is selected to be the updated mapping matrix. They are macro-average precision (MP), macro-average 𝑛 recall (MR), and macro-average F-measure (MF). 𝑗 𝑇 𝑀 = argmin ∑ ‖𝑋𝑖 − 𝐺𝑖 𝑀 𝑗 𝐶 𝑗 ‖ 𝑗 (7) For CMIRC, we compare different settings of cluster 𝑀𝑗 2 number for each view from 2 to 5 to find the one with best F- 𝑖=1  Fix 𝐺, 𝐶 𝑗 , 𝑀 𝑗 and update 𝐷 𝑗 measure. For the topics “iPhone” and “PlayStation”, (3, 2, 3) 𝐷 𝑗 is introduced to aid solving the optimization problem in for topic, view, sentiment view and popularity view is the Equation (4) and it can be calculated directly from 𝐺, 𝐶 𝑗 , 𝑀 𝑗 best one, while for the topics “Samsung Galaxy” and “Xbox”, according to Equations (3). (3, 5, 5) is the best one. The cluster number for each view on Of the four steps in CMIRC iterations, three are convex two-view clustering CMIRC and MIRC are also set the same problems related to one variable. It can be proved that each is as CMIRC. And for BKC, CKC and CSC, the cluster number is set the same as the global cluster number 5. guaranteed to converge to an optimal solution. Once the global clusters are ready, we select the labels of the users who 32 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina Table 3: Performance evaluation Topic iPhone Galaxy Xbox PlayStation Approach MP MR MF MP MR MF MP MR MF MP MR MF Combined BKC 0.2551 0.3526 0.1551 0.2725 0.2575 0.1443 0.2063 0.2340 0.0901 0.2964 0.3095 0.1467 view CKC 0.3366 0.3518 0.2649 0.3529 0.3314 0.1526 0.2419 0.2152 0.1585 0.2803 0.3407 0.2026 NMFMC 0.3627 0.4371 0.3465 0.3497 0.3568 0.2154 0.2874 0.2839 0.2770 0.3892 0.3170 0.2812 Multi-view MKC 0.3404 0.2983 0.1979 0.4132 0.3253 0.3155 0.3035 0.2960 0.2436 0.3333 0.3393 0.2328 CMIRC 0.4670 0.5056 0.4020 0.4914 0.3417 0.3616 0.4338 0.3337 0.3207 0.4031 0.3676 0.3531 MIRC 0.4200 0.3731 0.3730 0.4012 0.3126 0.3298 0.3352 0.3074 0.2914 0.3752 0.3477 0.3065 CSCtopic 0.2667 0.4552 0.2546 0.2367 0.3585 0.1542 0.1957 0.1898 0.1530 0.2745 0.2176 0.1809 Constrained CSCsentiment 0.2357 0.2527 0.1341 0.2256 0.1087 0.1417 0.2141 0.2036 0.1436 0.2044 0.2064 0.1007 Single-view CSCaccount 0.2628 0.3525 0.2270 0.3108 0.3179 0.2868 0.3236 0.1160 0.1376 0.2520 0.2088 0.1133 CMIRCts 0.2812 0.3240 0.1746 0.2977 0.2065 0.1879 0.4183 0.2761 0.2781 0.2971 0.2156 0.1903 Constrained CMIRCsa 0.2988 0.4559 0.3050 0.4386 0.3435 0.2917 0.2850 0.2630 0.2439 0.2466 0.2231 0.1993 Two-view CMIRCta 0.3555 0.4230 0.3220 0.4066 0.3330 0.2987 0.3908 0.2952 0.2879 0.3419 0.2578 0.2474 For another parameter 𝛼𝑗 , it is set to make all single views Moreover, By comparing constrained clustering approaches have balanced contributions to the final clustering results. We with single-view, two-view, and three-view, we observe that compute 𝛼𝑗 based on the average 2 -norm distance, i.e., 𝑑𝑖𝑠𝑗 , the performance gets better when more views are involved. It shows that the three views including topic, sentiment and between a user and all other users in view j. 𝛼𝑗 is negatively popularity views are all necessary to identify influence roles. related to 𝑑𝑖𝑠𝑗 . That is, At last, in three single-view constrained K-means clustering 𝑗 𝑗 𝑑𝑖𝑠𝑗 = ∑𝑛𝑖=1 ∑𝑛𝑘=𝑖+1‖𝑋𝑖 − 𝑋𝑘 ‖2 approaches, it is difficult to distinguish which view is better. and (8) However, when compare three two-view constrained 𝛼1 𝑑𝑖𝑠1 = 𝛼2 𝑑𝑖𝑠2 = 𝛼3 𝑑𝑖𝑠3 , 𝑠. 𝑡. ∑3𝑗=1 𝛼𝑗 = 1 clustering approaches, we find that the combination of the This gives us (0.177, 0.621, 0.202), (0.086, 0.588, 0.326), topic view and the popularity view performs the best, (0.093, 0.604, 0.303) and (0.180, 0.618, 0.202) for the topics followed by the combination of the sentiment view and the “iPhone”, “Samsung Galaxy, “Xbox” and “PlayStation”. The popularity view. The importance of user’s popularity in parameters 𝛼 for CMIRC on two-view clustering are set identifying influence roles is clear. Meanwhile, topic view analogously. The parameters used in MKC and NMFMC to and sentiment view are still important and necessary to balance the relative weights among different views are also supplement the popularity view. turned for their best performance. The constraints in all the To provide a more intuitive understanding of what are the constrained approaches are used in the same way. We assign users with each influence role look like, we provide the the labels of constrained users as the roles of the cluster centers to illustrate the characteristics of each role in corresponding clusters for all constrained clustering each view in Tables 4 to 6. We present the five most approaches. For BKC, MKC and NMFMC, we choose the representative (popular) words used by the users in each role assignment that maximizes the MF as the mapping of the and the ratio of average positive score and positive score of clusters to the influence roles. We repeat the experiments for all the users belong to the same role. The ratio is bigger if in all the approaches 10 times using random initialization and general people are more positive. We also give the average present their average performance in the Table 3. The numbers of followers and followees, and the percentage of performance of the proposed CMIRC consistently beat all the verified accounts for reference. The general feelings from others in all three metrics. the topic view analysis are (1) enthusiasts and celebrities tend Besides, we note that all multi-view clustering approaches to share their own experiences and assessments with the outperform the baseline BKC, and CMIRC beats the CKC. It words like “buy” and “love”; (2) experts who care more about demonstrates the power of multi-view clustering approaches specific aspects like to mention the detailed words such as and verifies that representing data in different views actually “charger” and “battery”; (3) the general words like “news” works for influence role detection. However, comparing and “mobile” are often used by information disseminators different multi-view clustering approaches, CMIRC and even who pass the latest news to people. From the sentiment view MIRC without constraints get more accurate results. It proves analysis, we do observe a significant trend that in general the rationality of our assumption that each view can only enthusiasts express more positively while information represent partial information, and by employing the disseminators hold more neutral sentiment. We can also see insufficient views together, we infer better global clustering that the popularity of celebrity is pretty high and it alone is results. Meanwhile, we also see that CMIRC performs better able to pick out celebrities easily. than MIRC that lacks of prior knowledge, which proves that building appropriate constraints to model the different 4 Conclusion influence role demands from a company is important. In this work, we address the issue of influence role detection. 33 Proceedings of the 1st International Workshop on Social Influence Analysis (SocInf 2015) July 27th, 2015 - Buenos Aires, Argentina We propose a Constrained Multi-view Influence Role constraints are used to model the prior information. The Clustering (CMIRC) approach to partition Twitter users into results indicate the effectiveness of our proposed approach. five clusters with three views of features (i.e., topic view, In the future, we will continue to explore more features to sentiment view and popularity view). In CMIRC, different capture their actual marketing effects on their followers. cluster numbers are allowed for different views and the Table 4: Role characteristics on topic view Enthusiast Information Disseminator Expert iPhone love, real, gaming, screen, battery news, apple, charger, battery, selling news, apple, charger, battery, selling Galaxy win, chance, space, buy, s5 chanlle fingerprint, android, 5s, tech, launch fingerprint, android, 5s, tech, launch Xbox play, game, enter, buy, lol 360, ps4, Microsoft, tv, coming white, china, flaw, security, sales PlayStation Game, play, win, lol, awesome Xbox, sony,coming, update,release sales, code, confirm, communiyy, console Table 5: Role characteristics on sentiment view iPhone Galaxy Topic Information Information View Enthusiast Celebrity Expert Enthusiast Celebrity Expert Disseminator Disseminator Positive 1.0702 3.34E-05 1.0702 0.0816 2.0 2.33E-08 0.7978 0.9997 Sentiment Negative 0.0772 3.74E-05 0.0772 0.1680 3.25E-09 1.58E-08 0.112 0.0003 Xbox PlayStation Positive 1.1178 3.78E-07 0.8545 0.0871 3.0 1.1426 0.0002 1.1426 sentiment Negative 0.083 2.45E-07 0.0898 1.110 7.38E-10 0.0852 0.0004 0.0852 Table 6: Role characteristics on popularity view Topic iPhone Galaxy View Information Information Enthusiast Celebrity Expert Enthusiast Celebrity Expert Disseminator Disseminator Follower 1800 1800 129968 1800 3157 2893 63537 2994 Popularity Followee 857 857 1866 857 997 1032 1538 995 isVerified 0 0 0.9999 0 0 0 0.9999 0 Xbox PlayStation Follower 3326 4066 185459 2666 1680 1680 169180 1680 Popularity Followee 905 1077 1448 968 365 365 738 365 isVerified 0 1.05E-06 1 0 2.24E-07 2.24E-07 1 2.24E-07 Influence in Twitter: The Million Follower Fallacy. 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