核参数判别选择方法在核主元分析中的应用

针对核主元分析(KPCA)中高斯核参数β的经验选取问题，提出了核主元分析的核参数判别选择方法。依据训练样本的类标签计算类内、类间核窗宽，在以上核窗宽中经判别选择方法确定核参数。根据判别选择核参数所确定的核矩阵，能够准确描述训练空间的结构特征。用主成分分析(PCA)对特征空间进行分解，提取主成分以实现降维和特征提取。判别核窗宽方法在分类密集区域选择较小窗宽，在分类稀疏区域选择较大窗宽。将判别核主成分分析(Dis-KPCA)应用到数据模拟实例和田纳西过程(TEP)，通过与KPCA、PCA方法比较，实验结果表明，Dis-KPCA方法有效地对样本数据降维且将三个类别数据100%分开,因此，所提方法的降维精度更高。

Application of kernel parameter discriminant method in kernel principal component analysis

In this paper, aiming at the priority selection of the Gaussian kernel parameter (β) in the Kernel Principal Component Analysis (KPCA), a kernel parameter discriminant method was proposed for the KPCA. It calculated the kernel window widths in the classes and between two classes for the training samples.The kernel parameter was determined with the discriminant method for the kernel window widths. The determined kernel matrix based on the discriminant selected kernel parameter could exactly describe the structure characteristics of the training space. In the end, it used Principal Component Analysis (PCA) to the decomposition for the feature space, and obtained the principal component to realize dimensionality reduction and feature extraction. The method of discriminant kernel window width chose smaller window width in the dense regions of classification, and larger window width in the sparse ones. The simulation of the numerical process and Tennessee Eastman Process (TEP) using the Discriminated Kernel Principle Component Analysis (Dis-KPCA) method, by comparing with KPCA and PCA, show that Dis-KPCA method is effective to the sample data dimension reduction and separates three classes of data by 100%,therefore, the proposed method has higher precision of dimension reduction.