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最小二乘支持向量机因模型学习过程中以二次损失函数为经验风险,造成学习结果对噪声特别敏感。鉴于实际问题中噪声不可避免、不可预测,且分布规律难寻,该文主要研究最小二乘支持向量机的鲁棒性增强算法,以提高其抵抗噪声与异常值的能力。通过分析得知,样本的局部异常因子与噪声大小间具有很大的相关性,因此提出了用于非线性回归问题的局部异常因子概念;并将其应用于最小二乘支持向量机模型学习时最优损失函数的确定中,提出了基于样本局部异常因子的直接加权最小二乘支持向量机鲁棒回归算法。为验证所提出算法的性能,该文最后以2个典型非线性对象为例,将其与原最小二乘支持向量机、文献中已有的基于预估噪声分布的加权最小二乘支持向量机进行了对比。对比结果表明,所提出的直接加权最小二乘支持向量机算法具有更好的鲁棒性。
Least Squares Support Vector Machines (SVMs) experience the risk of quadratic loss due to model learning, resulting in learning results that are particularly sensitive to noise. In view of the fact that noise is unavoidable, unpredictable and hard to find in distribution, this paper mainly studies the robust enhancement algorithm of least square support vector machine to improve its ability to resist noise and outliers. The analysis shows that the local anomaly factor of the sample is highly correlated with the noise level. Therefore, the concept of the local anomaly factor for nonlinear regression is proposed and applied to the least square support vector machine model learning In the determination of optimal loss function, a direct weighted least square support vector machine robust regression algorithm based on sample local anomaly factors is proposed. In order to verify the performance of the proposed algorithm, the paper finally takes two typical nonlinear objects as examples, compares it with the original least square support vector machine, the existing weighted least square support vector machine based on the estimated noise distribution in the literature Made a contrast. The comparison results show that the proposed direct weighted least squares support vector machine algorithm has better robustness.