Abstract
Nonlinear dimensionality reduction (DR) techniques offer the possibility to visually inspect a given finite high-dimensional data set in two dimensions. In this contribution, we address the problem to visualize a trained classifier on top of these projections. We investigate the suitability of popular DR techniques for this purpose and we point out the benefit of integrating auxiliary information as provided by the classifier into the pipeline based on the Fisher information.
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
Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Computation 12, 2385–2404 (2000)
Bunte, K., Biehl, M., Hammer, B.: A general framework for dimensionality reducing data visualization mapping. Neural Computation 24(3), 771–804 (2012)
Bunte, K., Schneider, P., Hammer, B., Schleif, F.-M., Villmann, T., Biehl, M.: Limited rank matrix learning, discriminative dimension reduction and visualization. Neural Networks 26, 159–173 (2012)
Caragea, D., Cook, D., Wickham, H., Honavar, V.G.: Visual methods for examining svm classifiers. In: Simoff, S.J., Böhlen, M.H., Mazeika, A. (eds.) Visual Data Mining. LNCS, vol. 4404, pp. 136–153. Springer, Heidelberg (2008)
Chang, C.-C., Lin, C.-J.: LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology 2, 27:1–27:27 (2011), Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
Cohn, D.: Informed projections. In: Becker, S., Thrun, S., Obermayer, K. (eds.) NIPS, pp. 849–856. MIT Press (2003)
Frank, A., Asuncion, A.: UCI machine learning repository (2010)
Gisbrecht, A., Hofmann, D., Hammer, B.: Discriminative dimensionality reduction mappings (2012)
Gisbrecht, A., Lueks, W., Mokbel, B., Hammer, B.: Out-of-sample kernel extensions for nonparametric dimensionality reduction. In: ESANN 2012, pp. 531–536 (2012)
Goldberger, J., Roweis, S., Hinton, G., Salakhutdinov, R.: Neighbourhood components analysis. In: Advances in Neural Information Processing Systems 17, pp. 513–520. MIT Press (2004)
Hernandez-Orallo, J., Flach, P., Ferri, C.: Brier curves: a new cost-based visualisation of classifier performance. In: International Conference on Machine Learning (June 2011)
Jakulin, A., Možina, M., Demšar, J., Bratko, I., Zupan, B.: Nomograms for visualizing support vector machines. In: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, KDD 2005, pp. 108–117. ACM, New York (2005)
Kohonen, T., Hynninen, J., Kangas, J., Laaksonen, J., Torkkola, K.: LVQ_PAK: The Learning Vector Quantization program package. Report A30, Helsinki University of Technology, Laboratory of Computer and Information Science (January 1996)
Kreßel, U.H.-G.: Advances in kernel methods. In: Chapter Pairwise Classification and Support Vector Machines, pp. 255–268. MIT Press, Cambridge (1999)
Lee, J.A., Verleysen, M.: Nonlinear dimensionality reduction. Springer (2007)
Ma, B., Qu, H., Wong, H.: Kernel clustering-based discriminant analysis. Pattern Recognition 40(1), 324–327 (2007)
Peltonen, J., Klami, A., Kaski, S.: Improved learning of riemannian metrics for exploratory analysis. Neural Networks 17, 1087–1100 (2004)
Poulet, F.: Visual svm. In: Chen, C.-S., Filipe, J., Seruca, I., Cordeiro, J. (eds.) ICEIS (2), pp. 309–314 (2005)
Roweis, S.: Machine learning data sets (2012), http://www.cs.nyu.edu/~roweis/data.html
Schulz, A., Gisbrecht, A., Bunte, K., Hammer, B.: How to visualize a classifier? In: New Challenges in Neural Computation, pp. 73–83 (2012)
Tenenbaum, J., da Silva, V., Langford, J.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)
van der Maaten, L., Hinton, G.: Visualizing high-dimensional data using t-sne. Journal of Machine Learning Research 9, 2579–2605 (2008)
Vellido, A., Martin-Guerroro, J., Lisboa, P.: Making machine learning models interpretable. In: ESANN 2012 (2012)
Venna, J., Peltonen, J., Nybo, K., Aidos, H., Kaski, S.: Information retrieval perspective to nonlinear dimensionality reduction for data visualization. Journal of Machine Learning Research 11, 451–490 (2010)
Wang, X., Wu, S., Wang, X., Li, Q.: Svmv - a novel algorithm for the visualization of svm classification results. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 968–973. Springer, Heidelberg (2006)
Ward, M., Grinstein, G., Keim, D.A.: Interactive Data Visualization: Foundations, Techniques, and Application. A. K. Peters, Ltd. (2010)
Weinberger, K.Q., Saul, L.K.: Unsupervised learning of image manifolds by semidefinite programming. Int. J. Comput. Vision 70(1), 77–90 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schulz, A., Gisbrecht, A., Hammer, B. (2013). Using Nonlinear Dimensionality Reduction to Visualize Classifiers. In: Rojas, I., Joya, G., Gabestany, J. (eds) Advances in Computational Intelligence. IWANN 2013. Lecture Notes in Computer Science, vol 7902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38679-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-38679-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38678-7
Online ISBN: 978-3-642-38679-4
eBook Packages: Computer ScienceComputer Science (R0)