Abstract
Partial rankings are totally ordered subsets of a set of items. They arise in different applications, such as clickstream analysis and collaborative filtering, but can be difficult to analyze with traditional data analysis techniques as they are combinatorial structures. We propose a method for creating scatterplots of sets of partial rankings by first representing them in a high-dimensional space and then applying known dimensionality reduction methods. We compare different approaches by using quantitative measures and demonstrate the methods on real data sets from different application domains. Despite their simplicity the proposed methods can produce useful visualizations that are easy to interpret.
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
Preview
Unable to display preview. Download preview PDF.
References
Demartines, P., Herault, J.: Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets. IEEE Transactions on Neural Networks 8(1), 148–154 (1997)
Fagin, R., Kumar, R., Mahdian, M., Sivakumar, D., Vee, E.: Comparing and aggregating rankings with ties. In: Proceedings of the 23rd ACM Symposium on Principles of Database Systems (PODS), ACM Press, New York (2004)
Gionis, A., Mannila, H., Puolamaki, K., Ukkonen, A.: Algorithms for discovering bucket orders from data. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data mining, pp. 561–566. ACM Press, New York (2006)
Kamishima, T., Akaho, S.: Efficient Clustering for Orders. In: Proceedings of The 2nd International Workshop on Mining Complex Data, pp. 274–278 (2006)
Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1991)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Ukkonen, A., Mannila, H.: Finding representative sets of bucket orders from partial rankings. review (submitted)
Venna, J., Kaski, S.: Local multidimensional scaling. Neural Networks 19(6-7), 889–899 (2006)
Venna, J., Kaski, S.: Nonlinear dimensionality reduction as information retrieval. In: Proceedings of the 11th International Conference on Artificial Intelligence and Statistics (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ukkonen, A. (2007). Visualizing Sets of Partial Rankings. In: R. Berthold, M., Shawe-Taylor, J., Lavrač, N. (eds) Advances in Intelligent Data Analysis VII. IDA 2007. Lecture Notes in Computer Science, vol 4723. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74825-0_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-74825-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74824-3
Online ISBN: 978-3-540-74825-0
eBook Packages: Computer ScienceComputer Science (R0)