关键词: 支持向量机, 多输入多输出, 主曲线, 交替优化, 流形正则化

Abstract: 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.

Key words: Support Vector Machine (SVM), Multi-Input-Multi-Output (MIMO), principal curve, alternating optimization, manifold regularization