Sentiment Analysis of User Comments in Online Mass Media and Forecasting the Dynamics of Their Sentiment Based on the Fokker–Planck Equation

J.P. Perova, S.A. Lesko, V.N. Kalinin

Abstract


A probabilistic sociodynamic model for forecasting user sentiment dynamics in online news media is proposed, based on the solution of the non-stationary Fokker – Planck equation. The dynamics of the comment graph state is described as a stochastic process comprising two components: a directed one (drift coefficient) and a random one (diffusion coefficient). A boundary value problem with absorbing boundary conditions describing the evolution of the comment graph state is formulated and solved analytically; expressions for the probability density and the probability of reaching a threshold state (percolation threshold) are obtained. Two cases of the initial state position relative to the percolation threshold are considered. It is shown that when the threshold is exceeded, a purposeful control action is required to ensure the predominance of directed influence over the stochastic component. A methodology for estimating model parameters from observed data using the Nelder – Mead optimization method is developed. An algorithm for forecasting and controlling the attainment of given threshold states of the network is presented, including monitoring, parametric identification, and estimation of the time to reach critical states. The model is verified using data from the VKontakte social network collected over 90 days. Forecasting accuracy for sentiment proportions is 5 – 19% (average 5% to 13%), and for average betweenness centrality values — 29 – 35%, which defines the applicability limits of the model for different graph characteristics.

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References


Dorogovtsev S. N., Mendes J. F. F. Evolution of networks // Advances in Physics. — 2002. — Vol. 51. — P. 1079–1187.

Newman M. E. J. The structure and function of complex networks // SIAM Review. — 2003. — Vol. 45. — P. 167–256.

Golder S. A., Wilkinson D. M., Huberman B. A. Rhythms of social interaction: messaging within a massive online network // Communities and Technologies. — 2007. — P. 41–66.

Sekara V., Stopczynski A., Lehmann S. Fundamental structures of dynamic social networks // Proceedings of the National Academy of Sciences. — 2016. — DOI: 10.1073/pnas.1602803113.

Airoldi E. M., Blei D. M., Fienberg S. E., Xing E. P. Mixed membership stochastic blockmodels // Journal of Machine Learning Research. — 2008. — Vol. 9. — P. 1981–2014.

Tran C., Shin W.-Y., Spitz A. Community detection in partially observable social networks // ACM Transactions on Knowledge Discovery from Data, 16(2), Article 22 (2022).. — DOI: 10.1145/3461339.

Mukhamediev R. I., Yakunin K., Mussabayev R. et al. Classification of negative information on socially significant topics in mass media // Symmetry. — 2020. — Vol. 12. — P. 1945. — DOI: 10.3390/sym12121945.

Willaert T., Van Eecke P., Beuls K., Steels L. Building social media observatories for monitoring online opinion dynamics // Social Media + Society. — 2020. — Vol. 6.

Bandari R., Asur S., Huberman B. A. The pulse of news in social media: forecasting popularity // arXiv preprint arXiv:1202.0332. — 2012.

Du B., Lian X., Cheng X. Partial differential equation modeling with Dirichlet boundary conditions on social networks // Boundary Value Problems. — 2018. — Vol. 2018, No. 50. — DOI: 10.1186/s13661-018-0964-4.

Liu X., He D., Liu C. Modeling information dissemination and evolution in time-varying online social network based on thermal diffusion motion // Physica A. — 2018. — Vol. 510. — P. 456–476.

Bomba A., Kunanets N., Pasichnyk V., Turbal Y. Mathematical and computer models of message distribution in social networks based on the space modification of Fermi–Pasta–Ulam approach // Advances in Intelligent Systems and Computing. — 2019. — Vol. 836. — P. 257–266.

Sahafizadeh E., Tork Ladani B. The impact of group propagation on rumor spreading in mobile social networks // Physica A. — 2018. — Vol. 506. — P. 412–423.

Lux T. Inference for systems of stochastic differential equations from discretely sampled data: a numerical maximum likelihood approach // Annals of Finance. — 2013. — Vol. 9, No. 2. — P. 217–248. — DOI: 10.1007/s10436-012-0219-9.

Hurn A., Jeisman J., Lindsay K. Teaching an old dog new tricks: improved estimation of the parameters of stochastic differential equations by numerical solution of the Fokker–Planck equation // Financial Econometrics Handbook / eds. Gregoriou G., Pascalau R. — London: Palgrave, 2010.

Orlov Yu. N., Fedorov S. L. Generation of nonstationary trajectories of a time series based on the Fokker–Planck equation. Proceedings of MIPT, 2016, vol. 8, no. 2, pp. 126–133.

Grimmett G. Percolation. — Berlin: Springer-Verlag, 1999. — 2nd ed.

Stauffer D., Aharony A. Introduction to Percolation Theory. — London: Taylor & Francis, 1992.

Zhukov D., Khvatova T., Lesko S., Zaltsman A. Managing social networks: applying the percolation theory methodology to understand individuals’ attitudes and moods // Technological Forecasting and Social Change, 129 (2018), 297–307 — DOI: 10.1016/j.techfore.2017.09.039.

Sigov A. S., Zhukov D. O., Khvatova T. Yu., Andrianova E. G. A model of forecasting of information events on the basis of the solution of a boundary value problem for systems with memory and self-organization // Journal of Communications Technology and Electronics. — 63, 1478–1485 (2018).— DOI: 10.1134/S1064226918120227.

Zhukov D., Khvatova T., Millar C., Zaltcman A. Modelling the stochastic dynamics of transitions between states in social systems incorporating self-organization and memory // Technological Forecasting and Social Change. — 2020. — Vol. 158. — P. 120134. — DOI: 10.1016/j.techfore.2020.120134.

Zhukov D., Perova J., Kalinin V. Description of the distribution law and non-linear dynamics of growth of comments number in news and blogs based on the Fokker–Planck equation // Mathematics. — 2022. — Vol. 10. — P. 989. — DOI: 10.3390/math10060989.

Perova Yu. P., Lesko S. A., Zhukov D. O., Chechurin A. V. Analysis and modeling of processes in complex social network structures based on the Fokker–Planck equation. Bulletin of Tomsk State University. Management, Computer Engineering and Informatics, 2022, no. 60, pp. 32–41. DOI: 10.17223/19988605/60/4.

Perova Yu. P., Grigoriev V. R., Zhukov D. O. Models and methods for the analysis of complex networks and social network structures. Russian Technological Journal, 2023, vol. 11, no. 2, pp. 33–49. DOI: 10.32362/2500-316X-2023-11-2-33-49.

Otradnov K. K., Perova Yu. P., Grigoriev V. R., Zhukov D. O. Analysis of time-series characteristics of sociodynamic processes in mass media user comment networks. Bulletin of RSREU, 2022, no. 82, pp. 147–161. DOI: 10.21667/1995-4565-2022-82-147-161.

Perova J. P., Kalinin V. N., Lesko S. A. Modeling the dynamics of changes in the number of comments of mass media users based on the Fokker–Planck equation and parameters of networks of their connections // International Journal of Open Information Technologies. — 2023. — Vol. 11, No. 4.


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