Abstract
Analytical applications in online social networks can be generalized as the influence evaluation problem, which targets at finding most influential users. Nowadays social influence evaluation is still an open and challenging issue. Most influence evaluation models focus on the single dimensional evaluation factor but fail to research on the multi-dimensional factors. In this paper, we propose a novel influence evaluation model: the temporal topic influence (TTI) evaluation model, which is a time-aware, content-aware and structure-aware evaluation model. For the aim of multi-dimensional evaluation, we incorporate multi-dimensional measure factors into our model, including the time factor, the topological information and the topic distribution information, etc. We propose a novel concept of user gravitational ability which is inspired by Newton’s law of universal gravitation. It can integrate multi-dimensional factors in an appropriate way. Our experiments are conducted on the Sina Weibo data set. Through the experimental analysis, we prove TTI model can calculate users’ influences effectively and efficiently. The TTI model can distinguish the value of users’ influences. And the TTI model identifies the top-k influential users with higher quality. We also validate the effect of time and topic measure factors in the influence evaluation process.
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Notes
A Chinese microblogging website, it is one of the most popular sites in China.
References
Facebook Stats. (2016). http://newsroom.fb.com/company-info.
Twitter Usage. (2016). https://about.twitter.com/company.
Kim, J., Lee, W., & Yu, H. (2014). CT-IC: Continuously activated and time-restricted independent cascade model for viral marketing. Knowledge-Based Systems, 62, 57–68.
Kempe, D., Kleinberg, J., & Tardos, É. (2003, August). Maximizing the spread of influence through a social network. In Proceedings of the ninth ACM SIGKDD international conference on knowledge discovery and data mining (pp. 137–146). ACM.
Bao, H., Li, Q., Liao, S. S., Song, S., & Gao, H. (2013). A new temporal and social PMF-based method to predict users’ interests in micro-blogging. Decision Support Systems, 55(3), 698–709.
Bodendorf, F., & Kaiser, C. (2009, November). Detecting opinion leaders and trends in online social networks. In Proceedings of the 2nd ACM workshop on social web search and mining (pp. 65–68). ACM.
Jiang, W., Wu, J., & Wang, G. (2015). On selecting recommenders for trust evaluation in online social networks. ACM Transactions on Internet Technology, 15(4), 14.
Golbeck, J., & Hendler, J. (2006). Inferring binary trust relationships in web-based social networks. ACM Transactions on Internet Technology (TOIT), 6(4), 497–529.
Xu, Z., Liu, Y., Mei, L., Luo, X., Hu, C., Zhang, H., et al. (2016). The mobile media based emergency management of web events influence in cyber-physical space. Wireless Personal Communications. doi:10.1007/s11277-016-3689-7.
Ma, T., Zhou, J., Tang, M., Tian, Y., Al-Dhelaan, A., Al-Rodhaan, M., et al. (2015). Social network and tag sources based augmenting collaborative recommender system. IEICE Transactions on Information and Systems, E98.D(4), 902–910.
Liu, B., Cong, G., Zeng, Y., Xu, D., & Chee, Y. M. (2014). Influence spreading path and its application to the time constrained social influence maximization problem and beyond. IEEE Transactions on Knowledge and Data Engineering, 26(8), 1904–1917.
Iribarren, J. L., & Moro, E. (2009). Impact of human activity patterns on the dynamics of information diffusion. Physical Review Letters, 103(3), 038702.
Saito, K., Kimura, M., Ohara, K., & Motoda, H. (2010). Selecting information diffusion models over social networks for behavioral analysis. Journal of the Optical Society of America B, 20(1), 91–96.
Chen, W., Wei, L., & Zhang, N. (2012). Time-critical influence maximization in social networks with time-delayed diffusion process. Chinese Journal of Engineering Design, 19(5), 340–344.
Tang, J., Sun, J., Wang, C., & Yang, Z. (2009, June). Social influence analysis in large-scale networks. In Proceedings of the 15th ACM SIGKDD international conference on knowledge discovery and data mining (pp. 807–816). ACM.
Weng, J., Lim, E. P., Jiang, J., & He, Q. (2010, February). Twitterrank: Finding topic-sensitive influential twitterers. In Proceedings of the third ACM international conference on web search and data mining (pp. 261–270). ACM.
Opsahl, T., Colizza, V., Panzarasa, P., & Ramasco, J. J. (2008). Prominence and control: The weighted rich-club effect. Physical Review Letters, 101(16), 168702.
Katona, Z., Zubcsek, P. P., & Sarvary, M. (2011). Network effects and personal influences: The diffusion of an online social network. Journal of Marketing Research, 48(3), 425–443.
Bakshy, E., Rosenn, I., Marlow, C., & Adamic, L. (2012, April). The role of social networks in information diffusion. In Proceedings of the 21st international conference on world wide web (pp. 519–528). ACM.
Wang, G., Jiang, W., Wu, J., & Xiong, Z. (2014). Fine-grained feature-based social influence evaluation in online social networks. IEEE Transactions on Parallel and Distributed Systems, 25(9), 2286–2296.
Almgren, K., & Lee, J. (2016). Applying an influence measurement framework to large social network. The Journal of Networking Technology, 7(1), 7.
Sun, B., & Ng, V. T. (2012). Identifying influential users by their postings in social networks. In International workshop on modeling social media (Vol. 8329, pp. 1–8). ACM.
Leavitt, A., Burchard, E., Fisher, D., & Gilbert, S. (2009). The influentials: New approaches for analyzing influence on twitter. Web Ecology Project, 4(2), 1–18.
Liu, X., Shen, H., Ma, F., & Liang, W. (2014). Topical influential user analysis with relationship strength estimation in Twitter. In IEEE international conference on data mining workshop (Vol. 26, pp. 1012–1019). IEEE.
Xiong, Z., Jiang, W., & Wang, G. (2012). Evaluating user community influence in online social networks. In IEEE, international conference on trust, security and privacy in computing and communications (pp. 640–647). IEEE.
Page, L., Brin, S., Motwani, R., & Winograd, T. (1998). The PageRank citation ranking: bringing order to the Web. Stanford InfoLab, 9, 1–14.
Xu, Z., Liu, Y., Zhang, H., Luo, X., Mei, L., & Hu, C. (2016). Building the multi-modal storytelling of urban emergency events based on crowdsensing of social media analytics. Mobile Networks and Applications. doi:10.1007/s11036-016-0789-2.
Zheng, N., Song, S., & Bao, H. (2015). A temporal-topic model for friend recommendations in Chinese microblogging systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 45(9), 1245–1253.
Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3(Jan), 993–1022.
Xu, Z., Zhang, S., Choo, K. K., Mei, L., Wei, X., Luo, X., et al. (2017). Hierarchy-cutting model based association semantic for analyzing domain topic on the web. IEEE Transactions on Industrial Informatics. doi:10.1109/TII.2017.2647986.
Hao, F. (2006). Application of Markov model in stock market forecast. Friend of Science Amateurs, 6(B), 62–63.
Blei, D. M. (2012). Probabilistic topic models. Communications of the ACM, 55(4), 77–84.
Ghosh, R., & Lerman, K. (2010). Predicting influential users in online social networks. arXiv preprint arXiv:1005.4882.
Lee, C., Kwak, H., Park, H., & Moon, S. (2010, April). Finding influentials based on the temporal order of information adoption in twitter. In Proceedings of the 19th international conference on world wide web (pp. 1137–1138). ACM.
Kiermer, V. (2006). Six degrees of separation. Nature Methods, 3(12), 964.
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China under Grant Numbers 61632009, 61472451, 61502161 and 61272151, and the High Level Talents Program of Higher Education in Guangdong Province under Funding Support Number 2016ZJ01.
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Appendix
Appendix
In this part, we show the explanation of \(G^s\) at first, and then we analyze and prove the time complexity of our algorithms.
1.1 Explanation of \(G^s\)
We conduct the experiments on our data sets and consult the Stanley Milgram’s experiments which called six degrees of separation [35]. The experiments both show the fact that two arbitrary users in the social network could become connected through six other users at most. We can get the further prove from previous research works. In model TTI, \(G^s\) denotes the user gravitation ability constant. The user gravitation ability always exists between two users, user u can attract user v under \(G^s\) in online social networks. In other words, user u can make an attraction to user v in any condition. Therefore, through the theory of six degrees of separation, we set the user gravitation ability constant 6.0 in this paper.
1.2 Proof of Theorem 1
Proof
Suppose n denotes the total number of users, m denotes the number of topics, e denotes the number of linked edges, \(|N_u|\) denotes the number of friends of user u, \(|N_v|\) denotes the number of friends of user v, and \(|C_{uv}|\) denotes the number of common friends between user u and v, at last a denotes the average degree of all users.
It is shown in Algorithm 1 at line 4, all topics should be considered for calculating the dynamic topic distribution P. It takes the complexity of O(m). At line 5, the shortest path between user u and v should be found. It will be time-consuming if we search p(u, v) from the the whole edge list P(u, v). We use the Bellman–Ford algorithm to calculate the shortest path and it takes the complexity of O(ne). For the connection distance at line 6, the time complexity is \(O(|C_{uv}|)\cdot (O(|N_u|)+O(|N_v|))\). The last three steps from line 7 to line 9 take constant complexity. In general, the complexity of lines 3–9 is \((O(m)+O(ne)+O(|C_{uv}|)\cdot (O(|N_u|)+O(|N_v|)))\). It is much larger than the real complexity, because users at the end of the calculation section have already finished some calculation parts such as, the topic distribution similarity, the shortest distance and the connection distance. In this case, we just take a time cost of \(O(|N_u|)\) for searching those values.
It can be easily understood that the average degree of all users a is much bigger than the number of average common friends. The size of the network is very big compared to the number of topic m. Thus, we can use the average degree a to replace \(O(|N_u|)\) and \(O(|N_v|)\), and O(m) and \(O(|C_{uv}|)\) can be neglected without loss of generality. As a result, the time complexity of Algorithm 1 is \(O(ne+a)\) per iteration.
Figure 5 shows that the distribution of user’s degree fits with the power-law distribution. So we can take the average degree a as a constant. We can deem the total time complexity of Algorithm 1 as O(ne) per iteration. \(\square\)
1.3 Proof of Theorem 2
Proof
In Algorithm 2 at line 3–6, we consider the adjustment process of TTI model. At line 5, we need to calculate the proportion \(p_{vu}\) that from user v to user u. But we have already get the results from Algorithm 1, it only need to search the results in the neighbor set of user v. Therefore, the time complexity is \(O(|N_v|)\) at line 5. Line 3 and line 6 both take constant time complexity of O(1). It takes a total of time complexity \(O(|N_u|\cdot |N_v|)\) for line 3–6.
The time complexity of each adjustment iteration (line 2–8) is \(O(n\cdot |N_u|\cdot |N_v|)\). As the reason shows in the proof of theorem 1, we use the average degree a to replace \(O(|N_u|)\) and \(O|N_v|)\). The time complexity of the adjustment calculation process is \(O(a^2 n)\) per iteration.
Since the same reason in the proof of theorem 1, we can take the average degree a as a constant. So the time complexity of Algorithm 2 is O(n) per iteration. \(\square\)
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Wang, F., Li, J., Jiang, W. et al. Temporal Topic-Based Multi-Dimensional Social Influence Evaluation in Online Social Networks. Wireless Pers Commun 95, 2143–2171 (2017). https://doi.org/10.1007/s11277-017-4047-0
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DOI: https://doi.org/10.1007/s11277-017-4047-0