Abstract: For the model selection issue of multiclass support vector machine (SVM), the authors presented a kernel evaluation criterion named multiclass kernel polarization (MKP) which was suitable for the multiclass classification scenario. Furthermore, an algorithm was proposed for selecting the parameters of the RBF kernel with multiple widths based on the optimization of the MKP criterion. Compared with the conventional exhaustive search method based on k-fold cross-validation, the proposed algorithm can automatically implement model selection procedure by using the gradient-based search technique, and hence overcome the disadvantages, such as strongly empirical and heavy computational burden. Experimental results on some UCI machine learning benchmark examples demonstrate the effectiveness of the multiclass kernel polarization and related algorithm for model selection with multiple parameters.

Key words: RBF kernel with multiple widths, multiclass kernel polarization, model selection, support vector machine (SVM), multiclass classification

摘要： 针对多类支持向量机的模型选择问题, 提出一种适用于多分类问题的核函数度量标准, 称为多类核极化。进一步地, 提出了基于优化该标准的多宽度RBF核的参数选择算法。与传统的基于k-折交叉验证的穷举搜索方法相比, 该算法利用基于梯度的搜索技术自动实现模型选择, 克服了传统方法的经验性强、计算量大的不足。UCI数据集上的实验结果验证了多类核极化与多参数模型选择算法的有效性。

关键词: 多宽度RBF核, 多类核极化, 模型选择, 支持向量机, 多类分类