Abstract
This work extends the rank aggregation framework for the setting of discovering optimal course sequences at the university level, and contributes to the literature on educational applications of network analysis. Each student provides a partial ranking of the courses taken throughout her or his undergraduate career. We build a network of courses by computing pairwise rank comparisons between courses based on the order students typically take them, and aggregate the results over the entire student population, to obtain a proxy for the rank offset between pairs of courses. We extract a global ranking of the courses via several state-of-the art algorithms for ranking with pairwise noisy information, including SerialRank, Rank Centrality, and the recent SyncRank based on the group synchronization problem. We test this application of rank aggregation on 15 years of student data from the Department of Mathematics at the University of California, Los Angeles (UCLA). Furthermore, we experiment with the above approach on different subsets of the student population conditioned on final GPA, and highlight several differences in the obtained rankings that uncover potential hidden pre-requisites in the Mathematics curriculum.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The research was reviewed and approved by the Chair of the UCLA Department of Mathematics, on fully anonymized data, allowing for the dissemination of our results in a scholarly publication.
References
Atkins, J.E., Boman, E.G., Hendrickson, B.: A spectral algorithm for seriation and the consecutive ones problem. SIAM J. Comput. 28(1), 297–310 (1998)
Bowen, R.M.: Science and Engineering Indicators 2012. National Science Foundation, Online, Arlington VA (2012)
Callaghan, T., Mucha, P.J., Porter, M.A.: Random walker ranking for NCAA division IA football. Am. Math. Mon. 114(9), 761–777 (2007)
Cucuringu, M.: Sync-Rank: robust ranking, constrained ranking and rank aggregation via eigenvector and SDP synchronization. IEEE Trans. Netw. Sci. Eng. 3(1), 58–79 (2016)
Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of the 10th International Conference on World Wide Web, pp. 613–622. ACM (2001)
Fogel, F., d’Aspremont, A., Vojnovic, M.: Serialrank: spectral ranking using seriation. In: Advances in Neural Information Processing Systems, pp. 900–908 (2014)
Ghauth, K.I., Abdullah, N.A.: Learning materials recommendation using good learners’ ratings and content-based filtering. Education. Tech. Research Dev. 58(6), 711–727 (2010)
Negahban, S., Oh, S., Shah, D.: Iterative ranking from pair-wise comparisons. In: NIPS, pp. 2474–2482 (2012)
Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: bringing order to the web. (1999)
Pei, J., Han, J., Wang, W.: Mining sequential patterns with constraints in large databases. In: Proceedings of the 11th International Conference on Information and Knowledge Management, pp. 18–25. ACM (2002)
Raman, K., Joachims, T.: Methods for ordinal peer grading. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1037–1046. ACM (2014)
Sayama, H.: Mapping the curricular structure and contents of network science courses. CoRR abs/1707.09570 (2017). http://arxiv.org/abs/1707.09570
Singer, A.: Angular synchronization by eigenvectors and semidefinite programming. Appl. Comput. Harmon. Anal. 30(1), 20–36 (2011)
Snyder, T.D., Dillow, S.A.: Digest of education statistics, 2012. National Center for Education Statistics (2013)
Thai-Nghe, N., Drumond, L., Krohn-Grimberghe, A., Schmidt-Thieme, L.: Recommender system for predicting student performance. Procedia Comput. Sci. 1(2), 2811–2819 (2010)
Wen-Shung Tai, D., Wu, H.J., Li, P.H.: Effective e-learning recommendation system based on self-organizing maps and association mining. Electron. Libr. 26(3), 329–344 (2008)
Xu, J., Xing, T., Van Der Schaar, M.: Personalized course sequence recommendations. IEEE Trans. Signal Process. 64(20), 5340–5352
Yang, J., Wang, W., Yu, P.S.: Mining asynchronous periodic patterns in time series data. IEEE Trans. Knowl Data Eng. 15(3), 613–628 (2003)
Yang, J., Wang, W., Yu, P.S., Han, J.: Mining long sequential patterns in a noisy environment. In: Proceedings of the 2002 ACM SIGMOD International Conference on Management of Data, pp. 406–417. ACM (2002)
Acknowledgements
This work was supported by NSF grant DMS-1045536, UC Lab Fees Research Grant 12-LR-236660, ARO MURI grant W911NF-11-1-0332, AFOSR MURI grant FA9550-10-1-0569, NSF grant DMS-1417674, and ONR grant N-0001-4121-0838, and EPSRC grant EP/N510129/1.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Cucuringu, M., Marshak, C.Z., Montag, D., Rombach, P. (2018). Rank Aggregation for Course Sequence Discovery. In: Cherifi, C., Cherifi, H., Karsai, M., Musolesi, M. (eds) Complex Networks & Their Applications VI. COMPLEX NETWORKS 2017. Studies in Computational Intelligence, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-72150-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-72150-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72149-1
Online ISBN: 978-3-319-72150-7
eBook Packages: EngineeringEngineering (R0)