Skip to main content
SpringerLink
Log in
Book cover

Computational Intelligence: Theories, Applications and Future Directions - Volume II pp 239–249Cite as

Hausdorff Distance-Based Binary Search Tree Multiclass Decomposition Algorithm

  • Conference paper
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 799))

Abstract

Multiclass decomposition algorithms are the means by which binary classification algorithms, like support vector machine, are used for multiclass classification problems. The popular multiclass decomposition algorithms, like one against one (OAO), one against all (OAA), perform the decomposition in a naive manner. This paper presents a novel heuristic-based decomposition algorithm that takes the Hausdorff distance between two classes to decide the decomposition. The presented algorithm has been evaluated and compared against OAO and OAA methods across nine datasets. The comparison shows that presented method not only provides comparable performance, but also in most cases can classify the test samples with fewer average number of support vectors, thus leading to faster test performance.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
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

Learn about institutional subscriptions

References

  1. Vapnik, V.: An overview of statistical learning theory. IEEE Trans. Neural Netw. 10(5) (1999)

    Google Scholar 

  2. Sevakula, R.K., Verma, N.K.: Assessing generalization ability of majority vote point classifiers. IEEE Trans. Neural Netw. Learn. Syst. (2016)

    Google Scholar 

  3. Hsu, C.W., Lin, C.J.: A comparison of methods for multiclass support vector machines. IEEE Trans. Neural Netw. 13(2), 415–425 (2002)

    Article  Google Scholar 

  4. Lorena, A.C., Carvalho, A.C.P.L.F., Gama, J.M.: A review on the combination of binary classifiers in multiclass problems. J. Artif. Intell. Rev. 30(1–4), 19–37 (2008)

    Google Scholar 

  5. Allwein, E.L., Shapire, R.E., Singer, Y.: Reducing multiclass to binary: a unifying approach for margin classifiers. In: Proceedings of the 17th International Conferences on Machine Learning, pp. 9–16 (2000)

    Google Scholar 

  6. Dietterich, T.G., Bariki, G.: Solving multiclass learning problems via error-correcting output codes. J. Artif. Intell. Res. 2, 263–286 (1995)

    Article  Google Scholar 

  7. Pimenta, E., Gama, J.: A study on error correcting output codes. In: Proceedings of the 2005 Portuguese conference on Artificial intelligence (EPIA’05), pp. 218–223 (2005)

    Google Scholar 

  8. Platt, J.C., Cristiani, N., Shawe-Taylor, J.: Large margin DAGs for multiclass classification. In: Proceedings of the Advances in Neural Information Processing Systems, pp. 547–553 (2000)

    Google Scholar 

  9. Kijsirikul, B., Ussivakul, N.: Multiclass support vector machines using adaptive directed acyclic graph. In: 2002 Proceedings of the International Joint Conference on Neural Networks, pp. 980–985 (2002)

    Google Scholar 

  10. Lei, H., Govindaraju, V.: Half-against-half multi-class support vector machines. In: Proceedings of the 6th International workshop on Multiple Classifier Systems, Seaside, CA, pp. 156–164 (2005)

    Google Scholar 

  11. Takahashi, F., Abe, S.: Decision-tree-based multiclass support vector machines. In: Proceedings of the 9th International Conferences Neural Information Processing (ICONIP’02), pp. 1418–1422 (2002)

    Google Scholar 

  12. Vural, V., Dy, J.G.: A hierarchical method for multi-class support vector machines. In: Proceedings of the 21st International Conferences on Machine Learning, Banff, pp. 831–838 (2004)

    Google Scholar 

  13. Lorena, A.C., Carvalho, A.C.P.L.F.: Minimum spanning trees in hierarchical multiclass support vector machines generation. In: International Conferences on Industrial, Engineering and Other Applications of Applied Intelligent Systems, pp. 422–431. Springer (2005)

    Google Scholar 

  14. Henrikson, J.: Completeness and total boundedness of the Hausdorff metric. MIT Undergrad. J. Math. 1, 69–80 (1999)

    Google Scholar 

  15. Scharf, L.: Computing the Hausdorff distance between sets of curves. Ph.D. thesis, Freie Universitat, Berlin (2003)

    Google Scholar 

  16. Sevakula, R.K., Verma, N.K.: Compounding general purpose membership functions for fuzzy support vector machine under noisy environment. IEEE Trans. Fuzzy Syst. (2017)

    Google Scholar 

  17. Chen, J., Wang, C.: Combining support vector machines with a pairwise decision tree. IEEE GeoSci. Remote Sens. Lett. 5(3), 409–413 (2008)

    Article  Google Scholar 

  18. Cortes, C., Vapnik, V.: Support vector networks. Mach. Learn. 20, 273–297 (1995)

    MATH  Google Scholar 

  19. Sevakula, R.K., Verma, N.K.: Support Vector Machine for Large Databases as Classifier. Springer SEMCCO 2012, pp. 303–313 (2012)

    Google Scholar 

  20. Sevakula, R.K., Verma, N.K.: Clustering based outlier detection in fuzzy SVM. In: 2014 IEEE International Conferences on Fuzzy Systems (FUZZ-IEEE’14), pp. 1172–1177 (2014)

    Google Scholar 

  21. Pujol, O., Radeva, P., Vitria, J.: Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes. IEEE Trans. Pattern Anal. Mach. Intell. 28(6), 1007–1012 (2006)

    Article  Google Scholar 

  22. Schwenker, F.: Hierarchical support vector machines for multi-class pattern recognition. In: Proceedings of the Fourth International Conferences on Knowledge-Based Intelligent Engineering Systems and Allied Technologies, pp. 561–565 (2000)

    Google Scholar 

  23. Shen, L., Tan, E.C.: Seeking better output-codes with genetic algorithm for multiclass cancer classification (Submitted to Bioinformatics)

    Google Scholar 

  24. Lin, C.-F., De Wang, S.: Fuzzy support vector machines. IEEE Trans. Neural Netw. 13(2), 464–471 (2002)

    Article  Google Scholar 

  25. Bordes, A.: Fast kernel classifiers with online and active learning. J. Mach. Learn. 1579–1619 (2005)

    Google Scholar 

  26. Crammer, K., Singer, Y.: On the learnability and design of output codes for multiclass problems. Comput. Learn. Theory 35–46 (2000)

    Google Scholar 

  27. Liu, B., Hao, Z., Tsang, E.C.C.: Nesting one-against-one algorithm based on SVMs for pattern classification. IEEE Trans. Neural Netw. 19(12), 2044–2052 (2008)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM India, Bengaluru, 560071, India

    Rahul Kumar Sevakula

  2. Indian Institute of Technology, Kanpur, Kanpur, 208016, India

    Nishchal K. Verma

Authors
  1. Rahul Kumar Sevakula
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nishchal K. Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rahul Kumar Sevakula .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Nishchal K. Verma

  2. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    A. K. Ghosh

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sevakula, R.K., Verma, N.K. (2019). Hausdorff Distance-Based Binary Search Tree Multiclass Decomposition Algorithm. In: Verma, N., Ghosh, A. (eds) Computational Intelligence: Theories, Applications and Future Directions - Volume II. Advances in Intelligent Systems and Computing, vol 799. Springer, Singapore. https://doi.org/10.1007/978-981-13-1135-2_19

Download citation

Publish with us

Policies and ethics

Search

Navigation