Skip to main content
SpringerLink
Log in

Outliers on Concept Lattices

  • Conference paper
  • First Online:
New Frontiers in Artificial Intelligence (JSAI-isAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8417))

Included in the following conference series:

  • 875 Accesses

Abstract

Outlier detection in mixed-type data, which contain both discrete and continuous features, is still a challenging problem. Here we newly introduce concept-based outlierness, which is defined on a hierarchy of clusters of data points and features, called the concept lattice, obtained by formal concept analysis (FCA). Intuitively, this outlierness is the degree of isolation of clusters on the hierarchy. Moreover, we investigate discretization of continuous features to embed the original continuous (Euclidean) space into the concept lattice. Our experiments show that the proposed method which detects concept-based outliers is more effective than other popular distance-based outlier detection methods that ignore the discreteness of features and do not take cluster relationships into account.

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

Access this chapter

Log in via an institution
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 EPUB and 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

Notes

  1. 1.

    http://research.nii.ac.jp/~uno/code/lcm.html

References

  1. Adda, M., Wu, L., White, S., Feng, Y.: Pattern detection with rare item-set mining. arXiv:1209.3089 (2012)

  2. Aggarwal, C.C.: Outlier Analysis. Springer, New York (2013)

    Book  Google Scholar 

  3. Bache, K., Lichman, M.: UCI machine learning repository (2013). http://archive.ics.uci.edu/ml

  4. Bay, S.D., Schwabacher, M.: Mining distance-based outliers in near linear time with randomization and a simple pruning rule. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 29–38 (2003)

    Google Scholar 

  5. Bhaduri, K., Matthews, B.L., Giannella, C.R.: Algorithms for speeding up distance-based outlier detection. In: Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 859–867 (2011)

    Google Scholar 

  6. Breunig, M.M., Kriegel, H.P., Ng, R.T., Sander, J.: LOF: identifying density-based local outliers. In: Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, pp. 93–104 (2000)

    Google Scholar 

  7. Caputo, B., Sim, K., Furesjo, F., Smola, A.: Appearance-based object recognition using SVMs: which kernel should I use? In: Proceedings of NIPS Workshop on Statistical Methods for Computational Experiments in Visual Processing and Computer Vision (2002)

    Google Scholar 

  8. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  9. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, New York (1998)

    MATH  Google Scholar 

  10. Hawkins, D.: Identification of Outliers. Chapman and Hall, London (1980)

    Book  Google Scholar 

  11. Kaytoue, M., Kuznetsov, S.O., Napoli, A.: Revisiting numerical pattern mining with formal concept analysis. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 1342–1347 (2011)

    Google Scholar 

  12. Knorr, E.M., Ng, R.T.: Algorithms for mining distance-based outliers in large datasets. In: Proceedings of the 24th International Conference on Very Large Data Bases, pp. 392–403 (1998)

    Google Scholar 

  13. Knorr, E.M., Ng, R.T., Tucakov, V.: Distance-based outliers: algorithms and applications. VLDB J. 8(3), 237–253 (2000)

    Article  Google Scholar 

  14. Liu, F.T., Ting, K.M., Zhou, Z.-H.: On detecting clustered anomalies using SCiForest. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds.) ECML PKDD 2010, Part II. LNCS, vol. 6322, pp. 274–290. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Makino, K., Uno, T.: New algorithms for enumerating all maximal cliques. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 260–272. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  16. Okubo, Y., Haraguchi, M.: An algorithm for extracting rare concepts with concise intents. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS, vol. 5986, pp. 145–160. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Orair, G.H., Teixeira, C.H.C., Wang, Y., Meira Jr., W., Parthasarathy, S.: Distance-based outlier detection: consolidation and renewed bearing. Proc. VLDB Endowment 3(1–2), 1469–1480 (2010)

    Article  Google Scholar 

  18. Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Efficient mining of association rules using closed itemset lattices. Inf. Syst. 24(1), 25–46 (1999)

    Article  Google Scholar 

  19. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing (2013). http://www.R-project.org

  20. Ramaswamy, S., Rastogi, R., Shim, K.: Efficient algorithms for mining outliers from large data sets. In: Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, pp. 427–438 (2000)

    Google Scholar 

  21. Schölkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J., Williamson, R.C.: Estimating the support of a high-dimensional distribution. Neural Comput. 13(7), 1443–1471 (2001)

    Article  Google Scholar 

  22. Sugiyama, M., Imajo, K., Otaki, K., Yamamoto, A.: Semi-supervised ligand finding using formal concept analysis. IPSJ Trans. Math. Model. Appl. (TOM) 5(2), 39–48 (2012)

    Google Scholar 

  23. Sugiyama, M., Yamamoto, A.: Semi-supervised learning on closed set lattices. Intell. Data Anal. 17(3), 399–421 (2013)

    Article  Google Scholar 

  24. Tsuiki, H.: Real number computation through Gray code embedding. Theor. Comput. Sci. 284(2), 467–485 (2002)

    Article  MathSciNet  Google Scholar 

  25. Valtchev, P., Missaoui, R., Godin, R.: Formal concept analysis for knowledge discovery and data mining: the new challenges. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 352–371. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Weihrauch, K.: Computable Analysis: An Introduction. Springer, New York (2000)

    Book  Google Scholar 

  27. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 314–339. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

Download references

Acknowledgments

This work is supported by the Alexander von Humboldt Foundation.

Author information

Authors and Affiliations

  1. Machine Learning and Computational Biology Research Group, Max Planck Institute for Intelligent Systems and Max Planck Institute for Developmental Biology, Tübingen, Germany

    Mahito Sugiyama

Authors
  1. Mahito Sugiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahito Sugiyama .

Editor information

Editors and Affiliations

  1. Seikei University, Musashino-shi, Tokyo, Japan

    Yukiko Nakano

  2. National Institute of Informatics Research Division, Tokyo, Japan

    Ken Satoh

  3. Ochanomizu University, Tokyo, Japan

    Daisuke Bekki

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Sugiyama, M. (2014). Outliers on Concept Lattices. In: Nakano, Y., Satoh, K., Bekki, D. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2013. Lecture Notes in Computer Science(), vol 8417. Springer, Cham. https://doi.org/10.1007/978-3-319-10061-6_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10061-6_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10060-9

  • Online ISBN: 978-3-319-10061-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation