计算机应用 ›› 2014, Vol. 34 ›› Issue (10): 2895-2898.DOI: 10.11772/j.issn.1001-9081.2014.10.2895

• 人工智能 • 上一篇    下一篇

核参数判别选择方法在核主元分析中的应用

张成,李娜,李元,逄玉俊   

  1. 沈阳化工大学 数理系,沈阳 110142;
  • 收稿日期:2014-05-06 修回日期:2014-06-19 出版日期:2014-10-01 发布日期:2014-10-30
  • 通讯作者: 李元
  • 作者简介:张成(1979-),男,辽宁沈阳人,讲师,博士研究生, 主要研究方向:系统监控、故障检测;李娜(1988-),女,辽宁朝阳人, 硕士研究生, 主要研究方向:故障诊断;李元(1964-),女,辽宁沈阳人,教授,博士生导师,主要研究方向:基于数据驱动的复杂过程故障检测与诊断;逄玉俊(1954-), 男,辽宁东港人,教授,主要研究方向:模式识别与智能系统、控制理论与工程、智能信息处理。
  • 基金资助:

    国家自然科学基金重点项目;国家自然科学基金资助项目;辽宁省教育厅科学研究项目;辽宁省博士启动基金资助项目

Application of kernel parameter discriminant method in kernel principal component analysis

ZHANG Cheng,LI Na,LI Yuan,PANG Yujun   

  1. Department of Science, Shenyang University of Chemical Technology, Shenyang Liaoning 110142, China;
  • Received:2014-05-06 Revised:2014-06-19 Online:2014-10-01 Published:2014-10-30
  • Contact: LI Yuan

摘要:

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。

Abstract:

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.

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