关键词: [&nu, ]-支持向量回归机, 无核二次曲面支持向量回归机, Pinball损失

Abstract:

An asymmetric [ν]- kernel-free quadratic surface support vector regression is proposed. By introducing the Pinball loss function, the training points above and below the[ε]band are given different penalties, so the better regression function is obtained. Furthermore, the parameters [p] and[ν]control the upper bound of the number of the training points classified incorrectly above and below the[ε]band. When [p=0.5], the method is degenerated into a symmetric [ν]-kernel-free quadratic surface support vector regression, and the number of support vectors which can be controlled by parameter[ν]is also proved. In fact, the algorithm is kernel free, thus avoiding the selection of kernel parameter without losing the interpretability of the decision function. The numerical experiment shows that the proposed approach has better fitting performance and less time consumption, and the parameter [p] will not increase the computational burden.

Key words: [ν]-support vector regression, kernel-free quadratic surface support vector regression, Pinball loss