Abstract
Support Vector Regression (SVR), which converts the original low-dimensional problem to a high-dimensional kernel space linear problem by introducing kernel functions, has been successfully applied in system modeling. Regarding the classical SVR algorithm, the value of the features has been taken into account, while its contribution to the model output is omitted. Therefore, the construction of the kernel space may not be reasonable. In the paper, a Feature-Weighted SVR (FW-SVR) is presented. The range of the feature is matched with its contribution by properly assigning the weight of the input features in data pre-processing. FW-SVR optimizes the distribution of the sample points in the kernel space to make the minimizing of the structural risk more reasonable. Four synthetic datasets and seven real datasets are applied. A superior generalization ability is obtained by the proposed method.
Highlights
Support Vector Regression (SVR) is a powerful kernel-based method for regression problems [1,2,3]
We concluded that the classical methods are not reasonable by analyzing the similarity of sample points in the kernel space; because the value of the features has been taken into account, while the contribution to the model output is omitted
We deduce that the contribution of the feature to the output is taken into account by Feature-Weighted SVR (FW-SVR), which reduces the influence of unimportant features on the kernel space feature
Summary
SVR is a powerful kernel-based method for regression problems [1,2,3]. It converts the original low-dimensional problem to a high-dimensional kernel space linear problem by introducing kernel functions. The generalization ability of the SVR model is determined by the kernel space feature [9]. The paper proposes an Feature-Weighted (FW)-SVR modeling method based on the kernel space feature. We concluded that the classical methods are not reasonable by analyzing the similarity of sample points in the kernel space; because the value of the features has been taken into account, while the contribution to the model output is omitted. A data pre-processing method of feature weighting based on the above conclusion is given. By adjusting the range of feature values by properly assigning the weight, the feature importance is matched with the influence of the kernel space, and the generalization ability of the model is improved.
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