Abstract:

Support vector regression based on multi-scale wavelet kernel has strong robustness and good generalization ability, but it is critical for it to choose appropriate model parameters.Obviously, the multi-scale kernel method has more difficulty in model selection than the single kernel approach.This paper proposed an approach about how to develop support vector regression based on mutli-scale wavelet kernel.It applied quantum clustering to data partition in order to determine the scale parameter of the multi-scale kernel, resorted to the support vector data description algorithm to calculate the kernel width of the corresponding data points, and then used cultural algorithms to optimize the kernel width and the remaining parameters.The results showed that the multi-scale kernel method outperformed the single wavelet approach and the Gaussian method.The experiments about three regression data sets—Boston housing, Bodyfat and Santa demonstrated that in contrast with the Gaussian approach, the present multi-scale wavelet support vector regression made the mean squared error of test sets decrease by 6.8%, 62.0% and 91.3%, respectively.Meanwhile, the proposed approach exhibited good generalization ability for propylene concentration estimation in the bottom byproduct of propylene fractionation tower.It not only enabled the model output of training set for propylene concentration to show little difference with the actual output, but also made the relative error of test set down to 0.211.Compared with other methods, it had the minimal prediction error.

Key words:

多尺度小波核, 量子聚类, 支持向量数据描述, 文化算法, 模型选择

摘要：

多尺度小波核支持向量回归方法具有较强的鲁棒性和较好的泛化能力，而模型选择是其获得良好泛化性能的关键，其中采用多尺度核方法参数选择的复杂度比单个核方法的参数选择大得多。这里提出了一种构造多尺度Morlet小波核的支持向量回归机的方法，它采用量子聚类方法划分样本类别以确定多尺度核的尺度个数，依赖支持向量数据描述方法对相应样本计算其核宽度，然后用文化算法优化剩下的少量模型参数。结果表明所得到的多尺度小波核模型的泛化能力明显优于单小波核或高斯核情形。分别用3个标准回归数据集Boston housing、Bodyfat和Santa作仿真，结果表明，相对于高斯核方法，多尺度小波核支持向量回归方法的测试集均方差分别减小了6.8%、62.0%和91.3%。同时，该方法对丙烯精馏塔的塔釜丙烯浓度预估表现出较好的泛化能力。它不仅使丙烯浓度训练集模型输出与实际输出基本吻合，而且使丙烯浓度测试集相对误差为0.211，与其他方法相比，其预测误差是最小的。

关键词:

多尺度小波核, 量子聚类, 支持向量数据描述, 文化算法, 模型选择