基于主曲线的多输入多输出支持向量机算法

Multi-input-multi-output support vector machine based on principal curve

针对传统多输入多输出(MIMO)支持向量机(SVM)没有考虑多个输出端之间依赖关系的问题,提出了一种新的基于主曲线的MIMO SVM算法。该算法基于所有输出端的模型参数位于一个流形上的假设,首先在现有的多维支持向量回归机(M-SVR)的基础上,构建一个流形正则化的优化目标,其中正则项为输出端模型参数到通过所有参数集合中间的主曲线的投影距离;其次,由于该优化目标为非凸,采用交替优化的方法,交替计算模型参数和参数集合的主曲线,直至收敛。采用仿真数据和实际的载荷识别工程数据进行验证,结果表明,与M-SVR和SVM单独建模方法相比,该算法可有效提高预测精度和数值稳定性。

To solve the problem that the traditional Multi-Input-Multi-Output （MIMO） Support Vector Machine （SVM） generally ignore the dependency among all outputs, a new MIMO SVM algorithm based on principal curve was proposed in this paper. Following the assumption that the model parameters of all outputs locate on a manifold, this paper firstly constructed a manifold regularization based on the Multi-dimensional Support Vector Regression （ M-SVR）, where the regularizer was the squared distance from the output parameters to the principal curve through the middle of all parameters＇ set. Secondly, considering the non-convexity of this regularization, this paper introduced an alternative optimization method to calculate the model parameters and principal curve in turn until convergence. The experiments on simulated data and real-life dynamic load identification data were conducted, and the results show that the proposed algorithm performs better than M-SVR and SVM based separate modeling method in terms of prediction precision and numerical stability.