# IMRank: influence maximization via finding self-consistent ranking

SIGIR, pp. 475-484, 2014.

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Keywords:

nonnumerical algorithms and problemscomplexity measuresiterative methodinfluence maximizationviral marketingMore(3+)

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Abstract:

Influence maximization, fundamental for word-of-mouth marketing and viral marketing, aims to find a set of seed nodes maximizing influence spread on social network. Early methods mainly fall into two paradigms with certain benefits and drawbacks: (1) Greedy algorithms, selecting seed nodes one by one, give a guaranteed accuracy relying on...More

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Introduction

- The prosperity of online social networks and social media invokes a new wave of research on social influence analysis [18, 8].
- Greedy algorithms provide a (1 − 1/e − ε) approximation by approximating influence spread through Monte Carlo simulation
- They have high computation cost, for the calculation of marginal influence spread invokes estimating the influence spread of nodes from scratch, using time-consuming Monte Carlo simulation.
- The latter, in contrast, resorts to estimate the influence spread via efficient heuristic methods.
- To the best of the knowledge, the authors lack an efficient and accurate algorithm of influence maximization for applications to large scale social networks in real world

Highlights

- The prosperity of online social networks and social media invokes a new wave of research on social influence analysis [18, 8]
- The first two subfigures give the results of influence spread under the weighted independent cascade model and the trivalency independent cascade model respectively, and the last one gives the results of running time
- We proposed an efficient iterative framework IMRank to explore the benefits of accurate greedy algorithms and efficient heuristic estimation of influence spread
- This framework effectively tunes any initial ranking into a self-consistent ranking in an iterative manner through fully leveraging the interplay between the ranking of nodes and their ranking-based marginal influence spread
- A last-to-first allocating strategy is further proposed to efficiently estimate the ranking-based marginal influence spread under the independent cascade model
- This strategy is elaborately designed according to the characteristics of the independent cascade model and the ranking-based marginal influence spread

Methods

- The authors evaluate IMRank on real-world networks by comparing IMRank with state-of-the-art influence maximization algorithms.

Results

- The authors evaluate IMRank on real-world networks by comparing it with state-of-the-art algorithms.
- Evaluation metrics include influence spread and running time.
- For the comparison of obtained influence spread, the authors test the cases of k = 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
- For the comparison of running time, the authors focus on the typical case k = 50.
- Each figure of Figures 5-8 shows the results on a certain network.
- The first two subfigures give the results of influence spread under the WIC model and the TIC model respectively, and the last one gives the results of running time

Conclusion

- The authors investigated influence maximization from a novel ranking perspective.
- The authors proposed an efficient iterative framework IMRank to explore the benefits of accurate greedy algorithms and efficient heuristic estimation of influence spread.
- This framework effectively tunes any initial ranking into a self-consistent ranking in an iterative manner through fully leveraging the interplay between the ranking of nodes and their ranking-based marginal influence spread.
- Its scalability outperforms the state-of-the-art heuristics while its accuracy is comparable to the greedy algorithms

Summary

## Introduction:

The prosperity of online social networks and social media invokes a new wave of research on social influence analysis [18, 8].- Greedy algorithms provide a (1 − 1/e − ε) approximation by approximating influence spread through Monte Carlo simulation
- They have high computation cost, for the calculation of marginal influence spread invokes estimating the influence spread of nodes from scratch, using time-consuming Monte Carlo simulation.
- The latter, in contrast, resorts to estimate the influence spread via efficient heuristic methods.
- To the best of the knowledge, the authors lack an efficient and accurate algorithm of influence maximization for applications to large scale social networks in real world
## Methods:

The authors evaluate IMRank on real-world networks by comparing IMRank with state-of-the-art influence maximization algorithms.## Results:

The authors evaluate IMRank on real-world networks by comparing it with state-of-the-art algorithms.- Evaluation metrics include influence spread and running time.
- For the comparison of obtained influence spread, the authors test the cases of k = 1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
- For the comparison of running time, the authors focus on the typical case k = 50.
- Each figure of Figures 5-8 shows the results on a certain network.
- The first two subfigures give the results of influence spread under the WIC model and the TIC model respectively, and the last one gives the results of running time
## Conclusion:

The authors investigated influence maximization from a novel ranking perspective.- The authors proposed an efficient iterative framework IMRank to explore the benefits of accurate greedy algorithms and efficient heuristic estimation of influence spread.
- This framework effectively tunes any initial ranking into a self-consistent ranking in an iterative manner through fully leveraging the interplay between the ranking of nodes and their ranking-based marginal influence spread.
- Its scalability outperforms the state-of-the-art heuristics while its accuracy is comparable to the greedy algorithms

- Table1: Notations
- Table2: Estimation on ranking-based marginal influence spread. MC indicates Monte Carlo simulation, and LAF indicates the LAF strategy
- Table3: Statistics of test networks

Related work

- Influence maximization problem was first studied by Domingos and Richardson from algorithmic perspective [6, 16]. Kempe et al then formulated it as a combinatorial optimization problem of finding a set of seed nodes with maximum influence spread [11]. They proved that this problem is NP-hard and proposed a greedy algorithm which can guarantee a (1 − 1/e − ε) approximation ratio. Here, ε is caused by the inaccurate estimation of influence spread. The biggest problem suffered by Kempe’s greedy algorithm is its low scalability, limiting it to social networks with small or moderate size.

Many efforts have been made to improve the scalability of Kempe’s greedy algorithm for influence maximization. “cost-effective lazy forward” (CELF) optimization strategy [13] and CELF++ [7] are proposed to reduce the times of influence spread estimation in Kempe’s greedy algorithm by exploiting the submodularity property of influence spread function. To reduce the number of Monte Carlo simulations, Chen et al [4] proposed NewGreedy algorithm and MixedGreedy algorithm. The NewGreedy algorithm reusing the results of Monte Carlo simulations in the same iteration to calculate marginal influence spread for all candidate nodes. Yet, it increases the computational cost for a single Monte Carlo simulation because the simulation is now conducted globally rather than locally as done in Kempe’s greedy algorithm. As a remedy, the MixedGreedy algorithm was developed, integrating the CELF strategy into the NewGreedy algorithm. Recently, Sheldon et al [17] proposed a sample average approximation approach from stochastic optimization for maximizing the spread of cascades under budget restriction. Cheng et al [5] proposed a StaticGreedy algorithm, remarkably reducing the number of Monte-Carlo simulations through strictly guaranteeing the submodularity and monotonicity properties of influence spread function. The above two works further improve the scalability of greedy algorithm effectively. These improvements can speedup the original greedy algorithm in several orders of magnitude, however, scalability is still a challenge for greedy algorithms.

Funding

- This work was funded by the National Basic Research Program of China (973 program) under grant numbers (2012CB316303, 2013CB329602), and the National Natural Science Foundation of China with Nos 61202215, 61174152, 61232010, 61202213, and 11305219

Reference

- L. Backstrom, D. Huttenlocher, J. Kleinberg, and X. Lan. Group formation in large social networks: membership, growth, and evolution. In KDD’06, pages 44–54, 2006.
- S. Brin and L. Page. The anatomy of a large-scale hypertextual web search engine. In WWW’98, pages 107–117, 1998.
- W. Chen, C. Wang, and Y. Wang. Scalable influence maximization for prevalent viral marketing in large-scale social networks. In KDD’10, pages 1029–1038, 2010.
- W. Chen, Y. Wang, and S. Yang. Efficient influence maximization in social networks. In KDD’09, pages 199–208, 2009.
- S. Cheng, H. Shen, J. Huang, G. Zhang, and X. Cheng. Staticgreedy: Solving the scalability-accuracy dilemma in influence maximization. In CIKM’13, 2013.
- P. Domingos and M. Richardson. Mining the network value of customers. In KDD’01, pages 57–66, 2001.
- A. Goyal, W. Lu, and L. V. Lakshmanan. Celf++: optimizing the greedy algorithm for influence maximization in social networks. In WWW’11, pages 47–48, 2011.
- J. Huang, X.-Q. Cheng, H.-W. Shen, T. Zhou, and X. Jin. Exploring social influence via posterior effect of word-of-mouth recommendations. In WSDM’12, WSDM ’12, pages 573–582, 2012.
- Q. Jiang, G. Song, C. Gao, Y. Wang, W. Si, and K. Xie. Simulated annealing based influence maximization in social networks. In AAAI’11, 2011.
- K. Jung, W. Heo, and W. Chen. Irie: Scalable and robust influence maximization in social networks. In ICDM’12, pages 918–923, 2012.
- D. Kempe, J. Kleinberg, and E. Tardos. Maximizing the spread of influence through a social network. In KDD’03, pages 137–146, 2003.
- M. Kimura, K. Saito, R. Nakano, and H. Motoda. Extracting influential nodes on a social network for information diffusion. Data Mining and Knowledge Discovery, 20(1):70–97, 2010.
- J. Leskovec, A. Krause, C. Guestrin, C. Faloutsos, J. VanBriesen, and N. Glance. Cost-effective outbreak detection in networks. In KDD’07, pages 420–429, 2007.
- M. Mathioudakis, F. Bonchi, C. Castillo, A. Gionis, and A. Ukkonen. Sparsification of influence networks. In KDD’11, pages 529–537, 2011.
- R. Narayanam and Y. Narahari. A shapley value-based approach to discover influential nodes in social networks. IEEE Transactions on Automation Science and Engineering, 8(1):130–147, 2011.
- M. Richardson and P. Domingos. Mining knowledge-sharing sites for viral marketing. In KDD’02, pages 61–70, 2002.
- D. Sheldon, B. Dilkina, A. N. Elmachtoub, R. Finseth, A. Sabharwal, J. Conrad, C. P. Gomes, D. Shmoys, W. Allen, O. Amundsen, and W. Vaughan. Maximizing the spread of cascades using network design. In UAI’10, pages 517–526, 2010.
- J. Tang, J. Sun, C. Wang, and Z. Yang. Social influence analysis in large-scale networks. In KDD’09, pages 807–816, 2009.
- C. Wang, W. Chen, and Y. Wang. Scalable influence maximization for independent cascade model in large-scale social networks. Data Mining and Knowledge Discovery, 25(3):545–576, 2012.
- Y. Wang, G. Cong, G. Song, and K. Xie. Community-based greedy algorithm for mining top-k influential nodes in mobile social networks. In KDD’10, pages 1039–1048, 2010.

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