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.
This work is partially supported by Grant-in-Aid for Young Scientists (Start-up, 20800045) from Japan Society for the Promotion of Science (JSPS).
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
Friedman, J.H.: Recent advances in predictive (machine) learning. Journal of Classification 23, 175–197 (2006)
Ware, C.: Information Visualization: Perception for Design, 2nd edn. Morgan Kaufmann, San Francisco (2004)
Battista, G.D., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Englewood Cliffs (1999)
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)
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)
Ware, C.: Designing with a 2 1/2D attitude. Information Design Journal 10(3), 171–182 (2001)
Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: WWW10, pp. 613–622. ACM, New York (2001)
Haraguchi, K., Hong, S., Nagamochi, H.: Classification by ordering data samples. RIMS Kokyuroku 1644, 20–34 (2009)
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)
Haraguchi, K., Hong, S., Nagamochi, H.: Visualization can improve multiple decision table classifiers. In: Proc. MDAI (2009) (to appear)
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)
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)
Dietterich, T.G., Bakiri, G.: Solving multiclass learning problems via error-correcting output codes. Journal of Artificial Intelligence Research 2, 263–286 (1995)
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)
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)
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
Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)
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/
Eades, P., Wormald, N.C.: Edge crossings in drawings of bipartite graphs. Algorithmica 11, 379–403 (1994)
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)
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)
Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM Journal on Algebraic and Discrete Methods 4, 312–316 (1983)
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)
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)
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
Crammer, K., Singer, Y.: On the algorithmic implementation of multiclass kernel-based vector machines. Journal of Machine Learning Research 2, 265–292 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haraguchi, K., Hong, SH., Nagamochi, H. (2010). Multiclass Visual Classifier Based on Bipartite Graph Representation of Decision Tables. In: Blum, C., Battiti, R. (eds) Learning and Intelligent Optimization. LION 2010. Lecture Notes in Computer Science, vol 6073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13800-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-13800-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13799-0
Online ISBN: 978-3-642-13800-3
eBook Packages: Computer ScienceComputer Science (R0)