Abstract
Preference data represent a particular type of ranking data where a group of people gives their preferences over a set of alternatives. Within this framework, distance-based decision trees represent a non-parametric tool for identifying the profiles of subjects giving a similar ranking. This paper aims at detecting, in the framework of (complete and incomplete) ranking data, the impact of the differently structured weighted distances for building decision trees. By means of simulations, we will compute the impact of higher/lower homogeneity in groups and different weighting structures both on splitting and on consensus ranking. The distances that will be used satisfy Kemeny’s axioms and, accordingly, a modified version of the rank correlation coefficient \(\tau _x\), proposed by Emond and Mason, will be proposed and used for rank aggregation and class label in the tree leaves.
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References
D’Ambrosio, A.: Tree based methods for data editing and preference rankings. Ph.D. thesis, Universitá degli Studi di Napoli “Federico II” (2007)
D’Ambrosio, A., Heiser, W.J.: A recursive partitioning method for the prediction of preference rankings based upon Kemeny distances. Psychometrika 81(3), 774–794 (2016)
Cook, W.D.: Distance based and ad hoc consensus models in ordinal preference ranking. Eur. J. Oper. Res. 172, 369–385 (2006)
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and regression trees. Chapman & Hall (1984)
Cheng, W., and Hühn, J., and Hüllermeier, E.: Decision tree and instance-based learning for label ranking. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 161–168 (2009)
Chen, J., Li, Y., Feng, L.: On the equivalence of weighted metrics for distance measures between two rankings. J. Inf. Comput. Sci. 11(13), 4477–4485 (2014)
D’Ambrosio, A., Amodio, S., Mazzeo, G.: ConsRank: compute the median ranking(s) according to the Kemeny’s axiomatic approach. R package version 2.0.1 (2017). https://CRAN.R-project.org/package=ConsRank
D’ambrosio, A., Amodio, S., Iorio, C.: Two algorithms for finding optimal solutions of the Kemeny rank aggregation problem for full rankings. Electron. J. Appl. Stat. Anal. 8(2), 198–213 (2015)
D’Ambrosio, A., Heiser, W.J.: A recursive partitioning method for the prediction of preference rankings based upon Kemeny distances. Psychometrika 81(3), 774–794 (2016)
Dittrich, R., Hatzinger, R., Katzenbeisser, W.: Modelling the effect of subject-specific covariates in paired comparison studies with an application to university rankings. J. R. Stat. Soc. C (Appl. Stat.) 47(4), 511–525 (1998)
Emond, E.J., Mason, D.W.: A new rank correlation coefficient with application to the concensus ranking problem. J. Multi-Criteria Decis. Anal. 11, 17–28 (2002)
García-Lapresta, J.L., Pérez-Román, D.: Consensus measures generated by weighted Kemeny distances on weak orders. In: Proceedings of the 10th International Conference on Intelligent Systems Design and Applications, Cairo (2010)
Henzgen, S., Hüllermeier, E.: Weighted rank correlation: a flexible approach based on fuzzy order relations. Jt. Eur. Conf. Mach. Learn. Knowl. Discov. Databases 422–437 (2015)
Irurozki, E., Calvo, B., Lozano, J.A.: PerMallows: an R package for mallows and generalized mallows models. J. Stat. Softw. 71(12), 1–30 (2016). https://doi.org/10.18637/jss.v071.i12
Kemeny, J.G., Snell, J.L.: Preference rankings an axiomatic approach. MIT Press (1962)
Kumar, R., Vassilvitskii, S.: Generalized Distances Between Rankings. In: Proceedings of the 19th International Conference on World Wide Web, WWW ’10, pp. 571–580. ACM, New York, NY, USA (2010)
Lee, P.H., Yu, P.L.H.: Distance-based tree models for ranking data. Comput. Stat. Data Anal. 54(6), 1672–1682 (2010)
Mallows, C.L.: Non-null ranking models. Biometrika 44(1–2), 114–130 (1957)
Piccarreta, R.: Binary trees for dissimilarity data. Comput. Stat. Data Anal. 54(6), 1516–1524 (2010)
Plaia, A., Sciandra, M.: Weighted distance-based trees for ranking data. In: Advances in Data Analysis and Classification, pp. 1–18. Springer, Berlin (2017) https://doi.org/10.1007/s11634-017-0306-x
Plaia, A., Buscemi, S., Sciandra, M.: A new position weight correlation coefficient for consensus ranking process without ties. Stat 8, e236 (2019). https://doi.org/10.1002/sta4.236
R Core Team, R.: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2018). https://www.R-project.org/
Strobl, C., Wickelmaier, F., Zeileis, A.: Accounting for individual differences in Bradley-Terry models by means of recursive partitioning. J. Educ. Behav. Stat. 36(2), 135–153 (2011)
Therneau, T., Clinic, M.: User written splitting functions for RPART (2015)
Therneau, T., Atkinson, B., Ripley, B.: rpart: recursive partitioning and regression trees. R package version 4.1–10 (2015)
Yilmaz, E., Aslam, J.A., Robertson, S.: A new rank correlation coefficient for information retrieval. In: Proceedings of the 31st Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 587–594 (2008)
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Plaia, A., Buscemi, S., Sciandra, M. (2023). Position Weighted Decision Trees for Ranking Data. In: Brentari, E., Chiodi, M., Wit, EJ.C. (eds) Models for Data Analysis. SIS 2018. Springer Proceedings in Mathematics & Statistics, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-031-15885-8_15
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