Advertisement

Multiclass Visual Classifier Based on Bipartite Graph Representation of Decision Tables

  • Kazuya Haraguchi
  • Seok-Hee Hong
  • Hiroshi Nagamochi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6073)

Abstract

In this paper, we consider K-class classification problem, a significant issue in machine learning or artificial intelligence. In this problem, we are given a training set of samples, where each sample is represented by a nominal-valued vector and is labeled as one of the predefined K classes. The problem asks to construct a classifier that predicts the classes of future samples with high accuracy. For K = 2, we have studied a new visual classifier named 2-class SE-graph based classifier (2-SEC) in our previous works, which is constructed as follows: We first create several decision tables from the training set and extract a bipartite graph called an SE-graph that represents the relationship between the training set and the decision tables. We draw the SE-graph as a two-layered drawing by using an edge crossing minimization technique, and the resulting drawing acts as a visual classifier. We can extend 2-SEC to K-SEC for K > 2 naturally, but this extension does not consider the relationship between classes, and thus may perform badly on some data sets. In this paper, we propose SEC-TREE classifier for K > 2, which decomposes the given K-class problem into subproblems for fewer classes. Following our philosophy, we employ edge crossing minimization technique for this decomposition. Compared to previous decomposition strategies, SEC-TREE can extract any tree as the subproblem hierarchy. In computational studies, SEC-TREE outperforms C4.5 and is competitive with SVM especially when K is large.

Keywords

Bipartite Graph Class Tree Numerical Attribute Decision Table Binary Attribute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Friedman, J.H.: Recent advances in predictive (machine) learning. Journal of Classification 23, 175–197 (2006)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Ware, C.: Information Visualization: Perception for Design, 2nd edn. Morgan Kaufmann, San Francisco (2004)Google Scholar
  3. 3.
    Battista, G.D., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Englewood Cliffs (1999)zbMATHGoogle Scholar
  4. 4.
    Haraguchi, K., Hong, S., Nagamochi, H.: Visual analysis of hierarchical data using 2.5D drawing with minimum occlusion. Poster session at IEEE PacificVis 2008 (2008)Google Scholar
  5. 5.
    Haraguchi, K., Hong, S., Nagamochi, H.: Visual analysis of hierarchical data using 2.5D drawing with minimum occlusion. Technical Report 2009-010, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan (2009)Google Scholar
  6. 6.
    Ware, C.: Designing with a 2 1/2D attitude. Information Design Journal 10(3), 171–182 (2001)CrossRefGoogle Scholar
  7. 7.
    Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: WWW10, pp. 613–622. ACM, New York (2001)Google Scholar
  8. 8.
    Haraguchi, K., Hong, S., Nagamochi, H.: Classification by ordering data samples. RIMS Kokyuroku 1644, 20–34 (2009)Google Scholar
  9. 9.
    Haraguchi, K., Hong, S., Nagamochi, H.: Classification via visualization of sample-feature bipartite graphs. Technical Report 2009-011, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan (2009)Google Scholar
  10. 10.
    Haraguchi, K., Hong, S., Nagamochi, H.: Visualization can improve multiple decision table classifiers. In: Proc. MDAI (2009) (to appear)Google Scholar
  11. 11.
    Haraguchi, K., Hong, S., Nagamochi, H.: Bipartite graph representation of multiple decision table classifiers. In: Watanabe, O., Zeugmann, T. (eds.) SAGA 2009. LNCS, vol. 5792, pp. 46–60. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Kohavi, R.: The power of decision tables. In: Lavrač, N., Wrobel, S. (eds.) ECML 1995. LNCS (LNAI), vol. 912, pp. 174–189. Springer, Heidelberg (1995)Google Scholar
  13. 13.
    Dietterich, T.G., Bakiri, G.: Solving multiclass learning problems via error-correcting output codes. Journal of Artificial Intelligence Research 2, 263–286 (1995)zbMATHGoogle Scholar
  14. 14.
    Kumar, S., Ghosh, J., Crawford, M.M.: Hierarchical fusion of multiple classifiers for hyperspectral data analysis. Pattern Analysis and Applications 5(2), 210–220 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Cheng, L., Zhang, J., Yang, J., Ma, J.: An improved hierarchical multi-class support vector machine with binary tree architecture. In: Proc. International Conference on Internet Computing in Science and Engineering, pp. 106–109 (2008)Google Scholar
  16. 16.
    Asuncion, A., Newman, D.: UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html
  17. 17.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
  18. 18.
    Witten, I.H., Frank, E.: Data Mining: Practical machine learning tools and techniques, 2nd edn. Morgan Kaufmann, San Francisco (2005), http://www.cs.waikato.ac.nz/ml/weka/ zbMATHGoogle Scholar
  19. 19.
    Eades, P., Wormald, N.C.: Edge crossings in drawings of bipartite graphs. Algorithmica 11, 379–403 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Transactions on Systems, Man, and Cybernetics SMC-11(2), 109–125 (1981)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Jünger, M., Mutzel, P.: 2-layer straightline crossing minimization: Performance of exact and heuristic algorithms. Journal of Graph Algorithms and Applications 1(1), 1–25 (1997)MathSciNetGoogle Scholar
  22. 22.
    Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM Journal on Algebraic and Discrete Methods 4, 312–316 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Weiss, S.M., Kulikowski, C.A.: Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Nets, Machine Learning, and Expert Systems. Morgan Kaufmann, San Francisco (1991)Google Scholar
  24. 24.
    Haraguchi, K., Nagamochi, H.: Extension of ICF classifiers to real world data sets. In: Okuno, H.G., Ali, M. (eds.) IEA/AIE 2007. LNCS (LNAI), vol. 4570, pp. 776–785. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Chang, C.C., Lin, C.J.: LIBSVM: a library for support vector machines (2001), Software available at: http://www.csie.ntu.edu.tw/~cjlin/libsvm
  26. 26.
    Crammer, K., Singer, Y.: On the algorithmic implementation of multiclass kernel-based vector machines. Journal of Machine Learning Research 2, 265–292 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kazuya Haraguchi
    • 1
  • Seok-Hee Hong
    • 2
  • Hiroshi Nagamochi
    • 3
  1. 1.Faculty of Science and EngineeringIshinomaki Senshu UniversityJapan
  2. 2.School of Information TechnologiesUniversity of SydneyAustralia
  3. 3.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityJapan

Personalised recommendations