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Kernel Fisher Discriminant Analysis Based on a Regularized Method for Multiclassification and Application in Lithological Identification

机译：基于正则化方法的核Fisher判别分析在岩性识别中的应用

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摘要

This study aimed to construct a kernel Fisher discriminant analysis (KFDA) method from well logs for lithology identification purposes. KFDA, via the use of a kernel trick, greatly improves the multiclassification accuracy compared with Fisher discriminant analysis (FDA). The optimal kernel Fisher projection of KFDA can be expressed as a generalized characteristic equation. However, it is difficult to solve the characteristic equation; therefore, a regularized method is used for it. In the absence of a method to determine the value of the regularized parameter, it is often determined based on expert human experience or is specified by tests. In this paper, it is proposed to use an improved KFDA (IKFDA) to obtain the optimal regularized parameter by means of a numerical method. The approach exploits the optimal regularized parameter selection ability of KFDA to obtain improved classification results. The method is simple and not computationally complex. The IKFDA was applied to the Iris data sets for training and testing purposes and subsequently to lithology data sets. The experimental results illustrated that it is possible to successfully separate data that is nonlinearly separable, thereby confirming that the method is effective.
机译：这项研究旨在从测井中构建核Fisher判别分析（KFDA）方法，以进行岩性识别。与Fisher判别分析（FDA）相比，KFDA通过使用内核技巧，大大提高了多分类准确性。 KFDA的最优核Fisher投影可以表示为广义特征方程。但是，很难求解特征方程。因此，使用正则化方法。在缺少确定正则化参数值的方法的情况下，通常根据专家的经验确定该参数或通过测试指定该参数。在本文中，建议使用改进的KFDA（IKFDA）通过数值方法获得最佳正则化参数。该方法利用了KFDA的最佳正则化参数选择能力来获得改进的分类结果。该方法简单且计算复杂。 IKFDA应用于虹膜数据集以进行培训和测试，随后又应用于岩性数据集。实验结果表明，可以成功地分离出非线性可分离的数据，从而证实该方法是有效的。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第17期|384183.1-384183.8|共8页
  • 作者

    Luo Dejiang; Liu Aijiang;

  • 作者单位

    Chengdu Univ Technol, Coll Management Sci, Chengdu 610059, Peoples R China.;

    Chengdu Univ Technol, Coll Geophys, Chengdu 610059, Peoples R China.;

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