模糊最小二乘支持向量机回归研究及应用

摘要

针对传统支持向量机对训练样本内的噪声和孤立点比较敏感，导致建模精度不高的问题，将模糊集理论引入到最小二乘支持向量机回归中，建立一种基于数据域描述的模糊最小二乘支持向量机回归的数学模型，该方法将样本映射到高维空间，在高维空间中寻找最小包含超球，然后根据样本到超球心的距离确定模糊隶属度的大小，通过仿真实验验证，该算法提高了支持向量机回归的训练精度，将此模型应用于谷氨酸发酵过程菌体浓度预测，结果表明此方法的有效性。%The traditional SVM is more sensitive to the noise and isolated points in training sample, and have lower modeling accuracy. In this paper, fuzzy set theory is introduced to least squares support vector regression, and then to establish a data domain description fuzzy least squares support vector machine regression. This method will sample mapped into a high dimensional space, and search a minimum enclosing sphere in high dimensional space. Meanwhile, according to the distance from sample to the center of the sphere, the size of fuzzy membership can be determined. A simulation experiment is provided to demonstrate that this algorithm can improve the accuracy of support vector machine regression. This model is applied to predict the concentration of glutamic acid bacteria fermentation process. Results we obtain in simulation show the effectiveness of the proposed approach.