Weighted solution path algorithm of support vector regression based on heuristic weight-setting optimization

In the conventional solution path algorithm of support vector regression, the ε-insensitive error of every training sample is equally penalized, which means every sample affects the generalization ability equally. However, in some cases, e.g. time series prediction or noisy function regression, the ε-insensitive error of the sample which could provide more important information should be penalized more heavily. Therefore, the weighted solution path algorithm of support vector regression is proposed in this paper. Error penalty parameter of each training sample is weighted differently, and the whole solution path is modified correspondingly. More importantly, by choosing Arc Tangent function as the prototype to generate weights with various characteristics, a heuristic weight-setting optimization algorithm is proposed to compute the optimal weights using particle swarm optimization (PSO). This method is applicable to different applications. Experiments on time series prediction and noisy function regression are conducted, demonstrating comparable results of the proposed weighted solution path algorithm and encouraging performance of the heuristic weight-setting optimization.