Advertisement

Rank Aggregation for Course Sequence Discovery

  • Mihai CucuringuEmail author
  • Charles Z. Marshak
  • Dillon Montag
  • Puck Rombach
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 689)

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.

Notes

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.

References

  1. 1.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bowen, R.M.: Science and Engineering Indicators 2012. National Science Foundation, Online, Arlington VA (2012)Google Scholar
  3. 3.
    Callaghan, T., Mucha, P.J., Porter, M.A.: Random walker ranking for NCAA division IA football. Am. Math. Mon. 114(9), 761–777 (2007)CrossRefzbMATHGoogle Scholar
  4. 4.
    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)MathSciNetCrossRefGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Fogel, F., d’Aspremont, A., Vojnovic, M.: Serialrank: spectral ranking using seriation. In: Advances in Neural Information Processing Systems, pp. 900–908 (2014)Google Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Negahban, S., Oh, S., Shah, D.: Iterative ranking from pair-wise comparisons. In: NIPS, pp. 2474–2482 (2012)Google Scholar
  9. 9.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: bringing order to the web. (1999)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    Sayama, H.: Mapping the curricular structure and contents of network science courses. CoRR abs/1707.09570 (2017). http://arxiv.org/abs/1707.09570
  13. 13.
    Singer, A.: Angular synchronization by eigenvectors and semidefinite programming. Appl. Comput. Harmon. Anal. 30(1), 20–36 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Snyder, T.D., Dillow, S.A.: Digest of education statistics, 2012. National Center for Education Statistics (2013)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Xu, J., Xing, T., Van Der Schaar, M.: Personalized course sequence recommendations. IEEE Trans. Signal Process. 64(20), 5340–5352Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    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)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mihai Cucuringu
    • 1
    • 2
    Email author
  • Charles Z. Marshak
    • 3
  • Dillon Montag
    • 4
  • Puck Rombach
    • 3
  1. 1.Department of Statistics and the Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.The Alan Turing InstituteLondonUK
  3. 3.Department of MathematicsUniversity of California at Los AngelesLos AngelesUS
  4. 4.Department of Computer ScienceWestmont CollegeSanta BarbaraUS

Personalised recommendations