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Robust linear programming discrimination of two linearly inseparable sets
Abstract
A single linear programming formulation is proposed which generates a plane that of minimizes an average sum of misclassified points belonging to two disjoint points sets in n-dimensional real space. When the convex hulls of the two sets are also disjoint, the plane completely separates the two sets. When the convex hulls intersect, our linear program, unlike all previously proposed linear programs, is guaranteed to generate some error-minimizing plane, without the imposition of extraneous normalization constraints that inevitably fail to handle certain cases. The effectiveness of the proposed linear program has been demonstrated by successfully testing it on a number of databases. In addition, it has been used in conjunction with the multisurface method of piecewise-linear separation to train a feed-forward neural network with a single hidden layer.
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Citations
Cited by
Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey
Murthy, S. K. (1998) · Data Mining and Knowledge Discovery · doi:10.1023/a:1009744630224 · Cited by 991
A new evolutionary system for evolving artificial neural networks
Yao, X., & Liu, Y. (1997) · IEEE Transactions on Neural Networks · doi:10.1109/72.572107 · Cited by 874
Cristianini, N., Kandola, J., Elisseeff, A., & Shawe-Taylor, J. (2006) · Studies in Fuzziness and Soft Computing · doi:10.1007/3-540-33486-6_8 · Cited by 837
Combining sparsity and rotational invariance in EEG/MEG source reconstruction
Haufe, S., Nikulin, V. V., Ziehe, A., Müller, K.-R., & Nolte, G. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.04.246 · Cited by 130
Metadata
- Authors
- Bennett, K. P., & Mangasarian, O. L.
- Venue
- Optimization Methods and Software
- Publisher
- Informa UK Limited
- Published
- 1992-01
- Volume
- 1
- Issue
- 1
- Pages
- 23-34
- ISSN
- 1026-7670 (ISSN-L)
- 1055-6788
- 1029-4937
- OpenAlex
- W2051381803
- Cited by
- 780
- References
- 0
- FWCI
- 7.15
- Type
- journal article
- Language
- en
- Open access
- closed
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- Bennett, K. P., & Mangasarian, O. L. (1992). Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software. https://doi.org/10.1080/10556789208805504
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
