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Self-defined information indices: application to the case of university rankings

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University rankings are now relevant decision-making tools for both institutional and private purposes in the management of higher education and research. However, they are often computed only for a small set of institutions using some sophisticated parameters. In this paper we present a new and simple algorithm to calculate an approximation of these indices using some standard bibliometric variables, such as the number of citations from the scientific output of universities and the number of articles per quartile. To show our technique, some results for the ARWU index are presented. From a technical point of view, our technique, which follows a standard machine learning scheme, is based on the interpolation of two classical extrapolation formulas for Lipschitz functions defined in metric spaces—the so-called McShane and Whitney formulae—. In the model, the elements of the metric space are the universities, the distances are measured using some data that can be extracted from the Incites database, and the Lipschitz function is the ARWU index.

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  • Aguillo, I., Bar-Ilan, J., Levene, M., & Ortega, J. (2010). Comparing university rankings. Scientometrics, 85(1), 243–256.

    Google Scholar 

  • Asadi, K., Dipendra, M., & Littman, M. L. (2018). Lipschitz continuity in model-based reinforcement learning. In Proceedings of the 35th International Conference on Machine Learning, Proc. Mach. Lear. Res., Vol. 80, pp. 264–273.

  • Bougnol, M. L., & Dulá, J. H. (2013). A mathematical model to optimize decisions to impact multi-attribute rankings. Scientometrics, 95(2), 785–796.

    Google Scholar 

  • Çakır, M. P., Acartürk, C., Alaşehir, O., & Çilingir, C. (2015). A comparative analysis of global and national university ranking systems. Scientometrics, 103(3), 813–848.

    Google Scholar 

  • Cancino, C. A., Merigó, J. M., & Coronado, F. C. (2017). A bibliometric analysis of leading universities in innovation research. Journal of Innovation & Knowledge, 2(3), 106–124.

    Google Scholar 

  • Chen, K.-H., & Liao, P.-Y. (2012). A comparative study on world university rankings: A bibliometric survey. Scientometrics, 92(1), 89–103.

    Google Scholar 

  • Cinzia, D., & Bonaccorsi, A. (2017). Beyond university rankings? Generating new indicators on universities by linking data in open platforms. Journal of the Association for Information Science and Technology, 68(2), 508–529.

    Google Scholar 

  • Cobzaş, Ş., Miculescu, R., & Nicolae, A. (2019). Lipschitz functions. Berlin: Springer.

    MATH  Google Scholar 

  • Deza, M. M., & Deza, E. (2009). Encyclopedia of distances. Berlin: Springer.

    MATH  Google Scholar 

  • 2019 U-Multirank ranking: European universities performing well.

  • Dobrota, M., Bulajic, M., Bornmann, L., & Jeremic, V. (2016). A new approach to the QS university ranking using the composite I-distance indicator: Uncertainty and sensitivity analyses. Journal of the Association for Information Science and Technology, 67(1), 200–211.

    Google Scholar 

  • Falciani, H., Calabuig, J. M., & Sánchez Pérez, E. A. (2020). Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial markets. Neurocomputing, 398, 172–184.

    Google Scholar 

  • Kehm, B. M. (2014). Global university rankings—Impacts and unintended side effects. European Journal of Education, 49(1), 102–112.

    Google Scholar 

  • Lim, M. A., & Øerberg, J. W. (2017). Active instruments: On the use of university rankings in developing national systems of higher education. Policy Reviews in Higher Education, 1(1), 91–108.

    Google Scholar 

  • Luo, F., Sun, A., Erdt, M., Raamkumar, A. S., & Theng, Y. L. (2018). Exploring prestigious citations sourced from top universities in bibliometrics and altmetrics: A case study in the computer science discipline. Scientometrics, 114(1), 1–17.

    Google Scholar 

  • Marginson, S. (2014). University rankings and social science. European Journal of Education, 49(1), 45–59.

    Google Scholar 

  • Pagell, R. A. (2014). Bibliometrics and university research rankings demystified for librarians. Library and information sciences (pp. 137–160). Berlin: Springer.

    Google Scholar 

  • Rao, A. (2015). Algorithms for Lipschitz extensions on graphs. Yale University: ProQuest Dissertations Publishing, 10010433.

  • Rosa, K. D., Metsis, V., & Athitsos, V. (2012). Boosted ranking models: A unifying framework for ranking predictions. Knowledge and Information Systems, 30(3), 543–568.

    Google Scholar 

  • Saisana, M., d’Hombres, B., & Saltelli, A. (2011). Rickety numbers: Volatility of university rankings and policy implications. Research Policy, 40(1), 165–177.

    Google Scholar 

  • Tabassum, A., Hasan, M., Ahmed, S., Tasmin, R., Abdullah, D. M., & Musharrat, T. (2017). University ranking prediction system by analyzing influential global performance indicators. In 2017 9th International Conference on Knowledge and Smart Technology (KST) (pp. 126–131) IEEE.

  • Van Raan, A. F. J., Van Leeuwen, T. N., & Visser, M. S. (2011). Severe language effect in university rankings: Particularly Germany and France are wronged in citation-based rankings. Scientometrics, 88(2), 495–498.

    Google Scholar 

  • von Luxburg, U., & Bousquet, O. (2004). Distance-based classification with Lipschitz functions. Journal of Machine Learning Research, 5, 669–695.

    MathSciNet  MATH  Google Scholar 

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The third and fourth authors gratefully acknowledge the support of the Ministerio de Ciencia, Innovación y Universidades (Spain), Agencia Estatal de Investigación, and FEDER, under Grant MTM2016-77054-C2-1-P. The first author gratefully acknowledge the support of Cátedra de Transparencia y Gestión de Datos, Universitat Politècnica de València y Generalitat Valenciana, Spain.

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Correspondence to A. Ferrer-Sapena.

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Ferrer-Sapena, A., Erdogan, E., Jiménez-Fernández, E. et al. Self-defined information indices: application to the case of university rankings. Scientometrics 124, 2443–2456 (2020).

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