Abstract
In this work, a new method for one-class classification based on the Convex Hull geometric structure is proposed. The new method creates a family of convex hulls able to fit the geometrical shape of the training points. The increased computational cost due to the creation of the convex hull in multiple dimensions is circumvented using random projections. This provides an approximation of the original structure with multiple bi-dimensional views. In the projection planes, a mechanism for noisy points rejection has also been elaborated and evaluated. Results show that the approach performs considerably well with respect to the state the art in one-class classification.
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
Bhattacharya, B.K.: Application of computational geometry to pattern recognition problems. PhD thesis (1982)
Toussaint, G.T.: The convex hull as a tool in pattern recognition. In: AFOSR Workshop in Communication Theory and Applications (1978)
Bennett, K.P., Bredensteiner, E.J.: Duality and geometry in svm classifiers. In: ICML, pp. 57–64 (2000)
Bi, J., Bennett, K.P.: Duality, geometry, and support vector regression. In: NIPS, pp. 593–600 (2002)
Takahashi, T., Kudo, M.: Margin preserved approximate convex hulls for classification. In: ICPR (2010)
Pal, S., Bhattacharya, S.: IEEE Transactions on Neural Networks 18(2), 600–605 (2007)
Mavroforakis, M.E., Theodoridis, S.: A geometric approach to support vector machine (svm) classification. Neural Networks, IEEE Transactions on 17, 671–682 (2006)
Zhou, X., Jiang, W., Tian, Y., Shi, Y.: Kernel subclass convex hull sample selection method for SVM on face recognition, vol.73 (2010)
Japkowicz, N.: Concept-learning in the absence of counter-examples: An autoassociation-based approach to classification. IJCAI, 518–523 (1995)
Tax, D.M.J.: One-class classification. PhD thesis (2001)
Preparata, F.P., Shamos, M.I.: Computational geometry: an introduction. Springer, New York.Inc (1985)
Johnson, W., Lindenstauss, J.: Extensions of lipschitz maps into a hilbert space. Contemporary Mathematics (1984)
Vempala, S.: The Random Projection Method. AMS (2004)
Blum, A.: Random projection, margins, kernels, and feature-selection. LNCS (2005)
Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning. In: NIPS, pp. 1313–1320 (2008)
Breiman, L.: Bagging predictors. Machine Learning 24, 123–140 (1996)
Frank, A., Asuncion, A.: UCI machine learning repository (2010)
Juszczak, P., Paclik, P., Pekalska, E., de Ridder, D., Tax, D., Verzakov, S., Duin, R.: A Matlab Toolbox for Pattern Recognition, PRTools4.1 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Casale, P., Pujol, O., Radeva, P. (2011). Approximate Convex Hulls Family for One-Class Classification. In: Sansone, C., Kittler, J., Roli, F. (eds) Multiple Classifier Systems. MCS 2011. Lecture Notes in Computer Science, vol 6713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21557-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-21557-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21556-8
Online ISBN: 978-3-642-21557-5
eBook Packages: Computer ScienceComputer Science (R0)