Abstract
We provide a framework for analyzing geographical influence networks that have impacts on visit event sequences for a set of point-of-interests (POIs) in a city. Since mutually-exciting Hawkes processes can naturally model temporal event data and capture interactions between those events, previous work presented a probabilistic model based on Hawkes processes, called CHP model, for finding cooperative structure among online items from their share event sequences. In this paper, based on Hawkes processes, we propose a novel probabilistic model, called RH model, for detecting geographical competitive structure in the set of POIs, and present a method of inferring it from the POI visit event history. We mathematically derive an analytical approximation formula for predicting the popularity of each of the POIs for the RH model, and also extend the CHP model so as to extract geographical cooperative structure. Using synthetic data, we first confirm the effectiveness of the inference method and the validity of the approximation formula. Using real data of Location-Based Social Networks (LBSNs), we demonstrate the significance of the RH model in terms of predicting the future events, and uncover the latent geographical influence networks from the perspective of geographical competitive and cooperative structures.
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Note that a similar formula can also be obtained for \({\overline{\lambda }}_u (t)\) of the SH model when \(g_k(t)\) does not depend on k.
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References
Blei, D., Frazier, P.: Distance dependent Chinese restaurant processes. J. Mach. Learn. Res. 12, 2461–2488 (2011)
Blundell, C., Heller, K., Beck, J.: Modelling reciprocating relationships with Hawkes processes. In: Proceedings of NIPS 2012, pp. 2600–2608 (2012)
Daneshmand, H., Gomez-Rodriguez, M., Song, L., Schölkopf, B.: Estimating diffusion network structures: recovery conditions, sample complexity & soft-thresholding algorithm. In: Proceedings of ICML 2014, pp. 793–801 (2014)
Farajtabar, M., Du, N., Gomez-Rodriguez, M., Valera, I., Zha, H., Song, L.: Shaping social activity by incentivizing users. In: Proceedings of NIPS 2014, pp. 2474–2482 (2014)
Farajtabar, M., Wang, Y., Gomez-Rodriguez, M., Li, S., Zha, H., Song, L.: Coevolve: a joint point process model for information diffusion and network evolution. J. Mach. Learn. Res. 18(41), 1–49 (2017)
Feng, S., Li, X., Zeng, Y., Cong, G., Chee, Y., Yuan, Q.: Personalized ranking metric embedding for next new poi recommendation. In: Proceedings of IJCAI 2015, pp. 2069–2075 (2015)
Gomez-Rodriguez, M., Leskovec, J., Krause, A.: Inferring networks of diffusion and influence. In: Proceedings of KDD 2010, pp. 1019–1028 (2010)
Hawkes, A.: Spectra of some self-exciting and mutually exiting point process. Biometrika 58(1), 83–90 (1971)
Junuthula, R., Haghdan, M., Xu, K., Devabhaktuni, V.: Block point process model for continuous-time event-based dynamic networks. In: Proceedings of WWW 2019, pp. 829–839 (2019)
Lin, P., Zhang, B., Guo, T., Wang, Y., Chen, F.: Interaction point processes via infinite branching model. In: Proceedings of AAAI 2016. pp. 1853–1859 (2016)
Linderman, S., Adams, R.: Discovering latent network structure in point process data. In: Proceedings of ICML 2014, pp. 1413–1421 (2014)
Matsutani, K., Kumano, M., Kimura, M., Saito, K., Ohara, K., Motoda, H.: Discovering cooperative structure among online items for attention dynamics. In: Proceedings of ICDMW 2017, pp. 1033–1041 (2017)
Neal, R.: Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Stat. 9(2), 249–265 (2000)
Ogata, Y.: On Lewis’ simulation method for point processes. IEEE Trans. Inform. Theory 27(1), 23–31 (1981)
Wang, H., Shen, H., Ouyang, W., Cheng, X.: Exploiting poi-specific geographical influence for point-of-interest recommendation. In: Proceedings of IJCAI 2018, pp. 3877–3883 (2018)
Yang, D., Zhang, D., Zheng, V., Yu, Z.: Modeling user activity preference by leveraging user spatial temporal characteristics in LBSNs. IEEE Trans. Syst. Man Cybern. Syst. 45(1), 129–142 (2015)
Yuan, B., Li, H., Bertozzi, A., Brantingham, P., Porter, M.: Multivariate spatiotemporal Hawkes processes and network reconstruction. SIAM J. Math. Data Sci. 1(2), 356–382 (2019)
Zhang, J., Chow, C.: Spatiotemporal sequential influence modeling for location recommendations: a gravity-based approach. ACM Trans. Intell. Syst. Technol. 7(1), 11:1–11:25 (2015)
Zhao, Q., Erdogdu, M., He, H., Rajaraman, A., Leskovec, J.: Seismic: a self-exciting point process model for predicting tweet popularity. In: Proceedings of KDD 2015, pp. 1513–1522 (2015)
Zhou, K., Zha, H., Song, L.: Learning social infectivity in sparse low-rank networks using multi-dimensional Hawkes processes. In: Proceedings of AISTATS 2013, pp. 641–649 (2013)
Acknowledgments
This work was supported in part by JSPS KAKENHI Grant Number JP17K00433 and Research Support Program of Ryukoku University.
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Fujii, T., Kumano, M., Gama, J., Kimura, M. (2021). Detecting Geographical Competitive Structure for POI Visit Dynamics. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-65351-4_3
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