Abstract
In this paper, we propose a reduction method for the multiobjective multiclass support vector machine (MMSVM), one of all-together method of the SVM. The method can maintain the discrimination ability, and reduce the computational complexity of the original MMSVM. First, we derive an approximate convex multiobjective optimization problem for the MMSVM by linearizing some constraints, and we secondly restrict the normal vectors of classifier candidates by using centroids obtained from the k-means clustering for each class dataset. The derived problem can be solved by the reference point method based on the centers of gravity of class datasets, in which the geometric margins between all pairs are exactly maximized. Some numerical experiments for benchmark problems show that the proposed method can reduce the computational complexity without decreasing its generalization ability widely.
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Tatsumi, K., Sugimoto, T., Kusunoki, Y. (2019). Approximate Multiobjective Multiclass Support Vector Machine Restricting Classifier Candidates Based on k-Means Clustering. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_23
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DOI: https://doi.org/10.1007/978-3-030-14815-7_23
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