基于KPCA和RS理论的支持向量分类机及其应用研究

Study on Application of Support Vector Machine for Classification Based on KPCA and RS Theory

核主成分分析KPCA是近年来提出的一个十分有效的数据降维方法,但它并不能保证所提取的第一主成分最适用于降维后的数据分类。粗糙集RS理论是处理这类问题的一个有效方法。提出一个基于KPCA与RS理论的支持向量分类机SVC,利用RS理论和信息熵原理对运用KPCA进行特征提取后的训练样本进行特征选择,保留重要特征,力求减小求解问题的规模,提高SVC的性能。在构建2006年上市公司财务困境预警模型的数值实验中,以KPCA、RS理论作为前置系统的SVC取得了良好效果。

Kernel Principle Component Analysis KPCA is one of the most effective methods for dimention reduction proposed in recent years. However, it does not guarantee that the selected first principle components will be the most adequate for classification. An effective solution dealing with this problem is to apply rough sets theory. This paper proposes a Support Vector Classifier SVC based on KPCA and Rough Sets Theory. In order to reduce the scale of the problem as well as improve the performance of SVC, the presented classifier implements a feature selection algorithm based on Rough Sets Theory and information entropy to reserve important features of dataset after feature extraction using KPCA. The numerical experiment of modeling financial distress early warning for listed companies shows the superior performance of this classifier.