Nothing Special   »   [go: up one dir, main page]

Skip to main content

Finding Total and Partial Orders from Data for Seriation

  • Conference paper
Discovery Science (DS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5255))

Included in the following conference series:

Abstract

Ordering and ranking items of different types (observations, web pages, etc.) are important tasks in various applications, such as query processing and scientific data mining. We consider different problems of inferring total or partial orders from data, with special emphasis on applications to the seriation problem in paleontology. Seriation can be viewed as the task of ordering rows of a 0-1 matrix so that certain conditions hold. We review different approaches to this task, including spectral ordering methods, techniques for finding partial orders, and probabilistic models using MCMC methods.

Joint work with Antti Ukkonen, Aris Gionis, Mikael Fortelius, Kai Puolamäki, and Jukka Jernvall.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agrawal, S., Chaudhuri, S., Das, G., Gionis, A.: Automated ranking of database query results. In: CIDR (2003)

    Google Scholar 

  2. Chaudhuri, S., Das, G., Hristidis, V., Weikum, G.: Probabilistic ranking of database query results. In: Proceedings of the 30th International Conference on Very Large Data Bases (VLDB) (2004)

    Google Scholar 

  3. 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) (2004)

    Google Scholar 

  4. Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA) (2003)

    Google Scholar 

  5. Fagin, R., Kumar, R., Sivakumar, D.: Efficient similarity search and classification via rank aggregation. In: Proceedings of the ACM Conference on Management of Data (SIGMOD) (2003)

    Google Scholar 

  6. Ilyas, I.F., Shah, R., Aref, W.G., Vitter, J.S., Elmagarmid, A.K.: Rank-aware query optimization. In: Proceedings of the ACM Conference on Management of Data (SIGMOD) (2004)

    Google Scholar 

  7. Li, C., Chang, K., Ilyas, I., Song, S.: Query algebra and optimization for relational top-k queries. In: Proceedings of the ACM Conference on Management of Data (SIGMOD) (2005)

    Google Scholar 

  8. Borodin, A., Roberts, G.O., Rosenthal, J.S., Tsaparas, P.: Link analysis ranking: Algorithms, theory, and experiments. ACM Transactions on Internet Technology 5(1) (2005)

    Google Scholar 

  9. Brin, S., Page, L.: The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems 30(1–7), 107–117 (1998)

    Article  Google Scholar 

  10. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of the 10th International World Wide Web Conference (WWW) (2001)

    Google Scholar 

  11. Haveliwala, T.: Topic-sensitive pagerank. In: Proceedings of the 11th International World Wide Web Conference (WWW) (2002)

    Google Scholar 

  12. Kleinberg, J.M.: Authoritative sources in a hyperlinked environment. Journal of the ACM 46(5) (1999)

    Google Scholar 

  13. Cohen, W.W., Schapire, R.E., Singer, Y.: Learning to order things. Journal of Artificial Intelligence Research 10, 243–270 (1999)

    MathSciNet  MATH  Google Scholar 

  14. Crammer, K., Singer, Y.: Pranking with ranking. In: Conference on Neural Information Processing Systems (NIPS) (2001)

    Google Scholar 

  15. Fürnkranz, J., Hüllermeier, E.: Pairwise preference learning and ranking. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS (LNAI), vol. 2837. Springer, Heidelberg (2003)

    Google Scholar 

  16. Lebanon, G., Lafferty, J.D.: Cranking: Combining rankings using conditional probability models on permutations. In: ICML (2002)

    Google Scholar 

  17. Gionis, A., Kujala, T., Mannila, H.: Fragments of order. In: KDD 2003 (2003)

    Google Scholar 

  18. Puolamäki, K., Fortelius, M., Mannila, H.: Seriation in paleontological data using Markov Chain Monte Carlo methods. PLoS Computational Biology 2(2) (February 2006)

    Google Scholar 

  19. Gionis, A., Mannila, H., Puolamaki, K., Ukkonen, A.: Algorithms for discovering bucket orders from data. In: KDD (2006)

    Google Scholar 

  20. Fortelius, M., Gionis, A., Jernvall, J., Mannila, H.: Spectral ordering and biochronology of european fossil mammals. Paleobiology 32(2), 206–214 (2006)

    Article  Google Scholar 

  21. Ukkonen, A.: Algorithms for Finding Orders and Analyzing Sets of Chains. PhD thesis, Helsinki University of Technology (2008)

    Google Scholar 

  22. Ukkonen, A., Mannila, H.: Finding outlying items in sets of partial rankings. In: Kok, J.N., Koronacki, J., López de Mántaras, R., Matwin, S., Mladenič, D., Skowron, A. (eds.) PKDD 2007. LNCS (LNAI), vol. 4702. Springer, Heidelberg (2007)

    Google Scholar 

  23. Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using P-Q tree algorithms. J. of Comp. and Syst. Sci. 13, 335–379 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hsu, W.L.: A simple test for the consecutive ones property. Journal of Algorithms 43 (2002)

    Google Scholar 

  25. Brower, J., Kile, K.: Seriation of an original data matrix as applied to palaeoecology. Lethaia 21, 79–93 (1988)

    Article  Google Scholar 

  26. Atkins, J.E., Boman, E.G., Hendrickson, B.: A spectral algorithm for seriation and the consecutive ones problem. SIAM Journal on Computing 28(1), 297–310 (1999)

    Article  MathSciNet  Google Scholar 

  27. Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems (2001)

    Google Scholar 

  28. Azar, Y., Fiat, A., Karlin, A.R., McSherry, F., Saia, J.: Spectral analysis of data. In: ACM Symposium on Theory of Computing (2000)

    Google Scholar 

  29. Chung, F.R.K.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics (1997)

    Google Scholar 

  30. Hill, M.: Correspondence analysis: A neglected multivariate method. Applied Statistics 23, 340–354 (1974)

    Article  Google Scholar 

  31. Kendall, D.G.: Abundance matrices and seriation in archaeology. Z. Wahscheinlichkeitstheorie verw. Geb. 17, 104–112 (1971)

    Article  MathSciNet  Google Scholar 

  32. Fortelius, M.: Neogene of the old world database of fossil mammals (NOW) (2006), http://www.helsinki.fi/science/now/

  33. Ukkonen, A., Fortelius, M., Mannila, H.: Finding partial orders from unordered 0-1 data. In: Proceedings of the 11th ACM Conference on Knowledge Discovery and Data Mining (KDD) (2005)

    Google Scholar 

  34. Mannila, H., Meek, C.: Global partial orders from sequential data. In: KDD (2000)

    Google Scholar 

  35. Wilf, H.S.: Generatingfunctionology. Academic Press, London (1994), http://www.math.upenn.edu/~wilf/DownldGF.html

    Google Scholar 

  36. Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC) (2005)

    Google Scholar 

  37. Coppersmith, D., Fleischer, L., Rudra, A.: Ordering by weighted number of wins gives a good ranking for weighted tournaments. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 776–782 (2006)

    Google Scholar 

  38. van Zuylen, A., Hegde, R., Jain, K., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. In: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 405–414 (2007)

    Google Scholar 

  39. Kempe, D., Kleinberg, J.M., Tardos, E.: Maximizing the spread of influence through a social network. In: KDD, pp. 137–146 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Berlin Heidelberg

About this paper

Cite this paper

Mannila, H. (2008). Finding Total and Partial Orders from Data for Seriation. In: Jean-Fran, JF., Berthold, M.R., Horváth, T. (eds) Discovery Science. DS 2008. Lecture Notes in Computer Science(), vol 5255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88411-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88411-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88410-1

  • Online ISBN: 978-3-540-88411-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics