Abstract
We propose a new formulation for the optimal separation problems. This robust formulation is based on finding the minimum volume ellipsoid covering the points belong to the class. Idea is to separate by ellipsoids in the input space without mapping data to a high dimensional feature space unlike Support Vector Machines. Thus the distance order in the input space is preserved. Hopfield Neural Network is described for solving the optimization problem. The benchmark Iris data is given to evaluate the formulation.
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
Vapnik, V.: Statistical Learning Theory. John Wiley, New York (1998)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)
Zhang, B.: Is the Maximal Margin Hyperplane Special in a Feature Space? Hewlett-Packard Research Laboratories Palo Alto (2001)
Barnes, E.R.: An Algorithm for Separating Patterns by Ellipsoids. IBM. J. Res. Develop. 26, 759–764 (1982)
Vandenberghe, L., Boyd, S.: Applications of Semidefinite Programming. Technical Report of California University (1998)
Glineur, F.: Pattern Separation Via Ellipsoids and Conic Programming, Mémoire de D.E.A., Faculté Polytechnique de Mons, Mons, Belgium (September 1998)
Astorino, A., Gaudioso, M.: Ellipsoidal Separation for Classification Problems. Optimizations Methods and Software 20, 267–276 (2005)
Doğan, H.: Gradient Networks Design for Clustering in Novel Optimization Frameworks. Dokuz Eylül University, PhD. Thesis (December 2004)
Kruss, M.: Nonlinear Multivariate Analysis with Geodesic Kernels. Berlin Technical University, Thesis (February 2002)
Zhang, Z.: Learning Metrics Via Discriminant Kernels and Multidimensional Scaling: To-ward Expected Euclidean Representation. In: ICML 2003, pp. 872–879 (2003)
Lyhyaoui, A., Martinez, M., Mora, I., Vaquez, M., Sancho, J.-L., Figueiras-Vidal, A.R.: Sample Selection Via Clustering to Construct Support Vector-Like Classifiers. IEEE Trans. Neural Networks 10, 1474–1481 (1999)
Tax, D.M.J., Duin, R.P.W.: Support Vector Domain Description. Pattern Recognition Letters 20, 1191–1199 (1999)
Vincent, W.: SVM and Co-Training. Honc Konc Bapist University, Technical Report (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Uçar, A., Demir, Y., Güzeliş, C. (2006). A New Formulation for Classification by Ellipsoids. In: Savacı, F.A. (eds) Artificial Intelligence and Neural Networks. TAINN 2005. Lecture Notes in Computer Science(), vol 3949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11803089_12
Download citation
DOI: https://doi.org/10.1007/11803089_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36713-0
Online ISBN: 978-3-540-36861-8
eBook Packages: Computer ScienceComputer Science (R0)