Fuzzy support vector machine based on hyperbolas optimized by the quantum-inspired gravitational search algorithm

Fuzzy support vector machines (FSVMs) are known for their excellent antinoise performance, but there is no general rule when the fuzzy membership function (FMF) is set up. A novel FSVM based on hyperbolas optimized by the quantum-inspired gravitational search algorithm (QGSH-FSVM) is proposed to handle this question. In the proposed QGSH-FSVM, the FMF is defined by two disparate hyperbolas, whose eccentricities are optimized by the quantum-inspired gravitational search algorithm. A variable called diversity, revealing the percentage of a sample in different classes, is proposed to distinguish outliers or noises from valid samples. Experimental results confirm that the QGSH-FSVM is able to provide the best solutions to different situations by optimizing its eccentricities. The traditional support vector machine and the FSVM based on affinity or the distance between a sample and its cluster center, however, can only succeed in some particular problems while failing in others.

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