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 智能系统学报  2019, Vol. 14 Issue (6): 1121-1126  DOI: 10.11992/tis.201905025 0

### 引用本文

LI Jingcan, DING Shifei. Twin support vector machine based on artificial fish swarm algorithm[J]. CAAI Transactions on Intelligent Systems, 2019, 14(6): 1121-1126. DOI: 10.11992/tis.201905025.

### 文章历史

1. 中国矿业大学 计算机科学与技术学院 江苏 徐州 221116;
2. 矿山数字化教育部工程研究中心，江苏 徐州 221116

Twin support vector machine based on artificial fish swarm algorithm
LI Jingcan 1,2, DING Shifei 1,2
1. School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China;
2. Mine Digitization Engineering Research Center of Minstry of Education of the People's Republic of China, Xuzhou 221116, China
Abstract: Twin support vector machine (TWSVM) is a machine learning algorithm based on the support vector machine. It has the advantages of fast training speed and superior classification performance. However, the algorithm cannot handle the parameter selection problem effectively, and the inappropriate parameters will reduce the classification ability. The artificial fish swarm algorithm (AFSA) is a group intelligent optimization algorithm with a strong global optimization ability and parallel processing capability. In this paper, TWSVM and AFSA are combined to solve the parameter selection problem of the TWSVM. First, the parameters of the support vector machine are taken as the position information of the artificial fish, and the classification accuracy is taken as the objective function. Then, the position and the optimal solution are updated by the artificial fish’s preying, swarming, following, and random behavior. At the end of the iterations, the optimal parameters and the optimal classification accuracy are obtained. The algorithm automatically determines the parameters of the TWSVM in the training process, avoiding the blindness of parameter selection, and improves the classification performance of the TWSVM
Key words: twin support vector machine    artificial fish swarm algorithm    pattern classification    parameter optimization    accuracy    swarm intelligence    quadratic programming    parallel processing    global optimization

1 相关理论 1.1 孪生支持向量机

 $K({{{x}}^{\rm{T}}},{{{C}}^{\rm{T}}}){{w}}{}_1 + {b_1} = 0,{\rm{ }}K({{{x}}^{\rm{T}}},{{{C}}^{\rm{T}}}){{w}}{}_2 + {b_2}{\rm{ = 0}}$ (1)

 $\begin{gathered} \mathop {\min }\limits_{{{w}_1},{{b}_1},{{\xi }_1}} \frac{1}{2}{\left\| {K({A},{{C}^{\rm{T}}}){{w}_1} + {{e}_1}{b_1}} \right\|^2} + {c_1}{e}_2^{\rm{T}}{{\xi }_2} \\ {\rm{s}}{\rm{.t}}{\rm{.\;- (}}K({B},{{C}^{\rm{T}}}){{w}_1} + {{e}_2}{b_1}) \geqslant {{e}_2} - {{\xi }_2},{{\xi }_2} \geqslant 0 \\ \end{gathered}$ (2)
 $\begin{gathered} \mathop {\min }\limits_{{{w}_2},{{b}_2},{{\xi }_2}} \frac{1}{2}{\left\| {K({B},{{C}^{\rm{T}}}){{w}_2} + {{e}_2}{b_2}} \right\|^2} + {c_2}{e}_1^{\rm{T}}{{\xi }_1} \\ {\rm{s}}{\rm{.t}}{\rm{. \;(}}K({A},{{C}^{\rm{T}}}){{w}_2} + {{e}_1}{b_2}) \geqslant {{e}_1} - {{\xi }_1},{{\xi }_1} \geqslant 0 \\ \end{gathered}$ (3)

 $K({{x}^{\rm{T}}},{{C}^{\rm{T}}}){w}{}_r + {b_r} = \mathop {\min }\limits_{i = 1,2} \left| {K({{x}^{\rm{T}}},{{C}^{\rm{T}}}){w}{}_i + {b_i}} \right|$ (4)

x属于第r类，其中 \$r \in \left\{ {1,2} \