Abstract
We propose a novel topology preserving self-organized map (SOM) classifier with transductive confidence machine (TPSOM-TCM). Typically, SOM acts as a dimension reduction tool for mapping training samples from a high-dimensional input space onto a neuron grid. However, current SOM-based classifiers can not provide degrees of classification reliability for new unlabeled samples so that they are difficult to be used in risk-sensitive applications where incorrect predictions may result in serious consequences. Our method extends a typical SOM classifier to allow it to supply such reliability degrees. To achieve this objective, we define a nonconformity measurement with which a randomness test can predict how nonconforming a new unlabeled sample is with respect to the training samples. In addition, we notice that the definition of nonconformity measurement is more dependent on the quality of topology preservation than that of quantization error reduction. We thus incorporate the grey relation coefficient (GRC) into the calculation of neighborhood radii to improve the topology preservation without increasing the quantization error. Our method is able to improve the time efficiency of a previous method kNN-TCM, when the number of samples is large. Extensive experiments on both the UCI and KDDCUP 99 data sets show the effectiveness of our method.
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
Ambwani, T.: Multi Class Support Vector Machine Implementation to Intrusion Detection. In: Proceedings of the International Joint Conference on Neural Networks (2003)
Barbará, D., Domeniconi, C., Rogers, J.P.: Detecting Outliers Using Transduction and Statistical Testing. In: KDD 2006: Proceedings of the Twelveth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2006)
Cho, S.B.: Incorporating Soft Computing Techniques into A Probabilistic Intrusion Detection System. IEEE Transactions on Systems, Man, and Cybernetics, Part C 32(2), 154–160 (2002)
Gammerman, A., Vovk, V.: Prediction Algorithms and Confidence Measures Based on Algorithmic Randomness Theory. Theor. Comput. Sci. 287(1), 209–217 (2002)
Hu, Y.C., Chen, R.S., Hsu, Y.T., Tzeng, G.H.: Grey Self-organizing Feature Maps. Neurocomputing 48(1-4), 863–877 (2002)
Kayacik, H.G., Zincir-Heywood, A.N., Heywood, M.I.: A Hierarchical SOM-based Intrusion Detection System. Eng. Appl. of AI 20(4), 439–451 (2007)
Kiviluoto, K.: Topology Preservation in Self-organizing Maps. In: IEEE International Conference on Neural Networks (1996)
Kohonen, T., Schroeder, M.R., Huang, T.S. (eds.): Self-Organizing Maps. Springer, Heidelberg (2001)
Martin, C., Diaz, N.N., Ontrup, J., Nattkemper, T.W.: Hyperbolic SOM-based Clustering of DNA Fragment Features for Taxonomic Visualization and Classification. Bioinformatics 24(14), 1568–1574 (2008)
Melluish, T., Saunders, C., Nouretdinov, I., Vovk, V.: Comparing the Bayes and Typicalness Frameworks. In: EMCL 2001: Proceedings of the Twelfth European Conference on Machine Learning, pp. 360–371 (2001)
Proedrou, K., Nouretdinov, I., Vovk, V., Gammerman, A.: Transductive Confidence Machines for Pattern Recognition. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) ECML 2002. LNCS (LNAI), vol. 2430, pp. 381–390. Springer, Heidelberg (2002)
Su, M.C., Chang, H.T., Chou, C.H.: A Novel Measure for Quantifying the Topology Preservation of Self-Organizing Feature Maps. Neural Process. Lett. 15(2), 137–145 (2002)
Suganthan, P.N.: Hierarchical Overlapped SOM’s for Pattern Classification. IEEE Transactions on Neural Networks 10(1), 193–196 (1999)
Vanderlooy, S., Maaten, L., Sprinkhuizen-Kuyper, I.: Off-Line Learning with Transductive Confidence Machines: An Empirical Evaluation. In: Perner, P. (ed.) MLDM 2007. LNCS (LNAI), vol. 4571, pp. 310–323. Springer, Heidelberg (2007)
Vanderlooy, S., Sprinkhuizen-Kuyper, I.: An Overview of Algorithmic Randomness and its Application to Reliable Instance Classification. Technical Report MICC-IKAT 07-02, Universiteit Maastricht (2007)
Villmann, T., Der, R., Herrmann, M., Martinetz, T.M.: Topology Preservation in Self-organizing Feature Map: Exact Definition and Measurement. IEEE Transactions on Neural Networks 8(2), 256–266 (1997)
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
Tong, B., Qin, Z., Suzuki, E. (2010). Topology Preserving SOM with Transductive Confidence Machine. In: Pfahringer, B., Holmes, G., Hoffmann, A. (eds) Discovery Science. DS 2010. Lecture Notes in Computer Science(), vol 6332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16184-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-16184-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16183-4
Online ISBN: 978-3-642-16184-1
eBook Packages: Computer ScienceComputer Science (R0)