A Modified Algorithm for Generalized Discriminant Analysis
A Modified Algorithm for Generalized Discriminant Analysis
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DOI：
10.1162/089976604773717612
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发表时间：
2004-06
影响因子：
2.9
通讯作者：
Wenming Zheng;Li Zhao;C. Zou
中科院分区：
文献类型：
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作者：
Wenming Zheng;Li Zhao;C. Zou
广义判别分析（GDA）是经典线性判别分析（LDA）通过核技巧从线性域到非线性域的推广。然而，在GDA的先前算法中，解可能遭受退化特征值问题（即，具有相同特征值的几个特征向量），这使得它们在判别能力方面不是最佳的。在这封信中，我们提出了一个改进的算法GDA（MGDA）来解决这个问题。MGDA方法的目的是消除GDA的退化，并找到最佳的鉴别解决方案，最大化的类间散布的子空间由GDA的退化特征向量。理论分析和在ORL人脸库上的实验结果表明，MGDA方法比GDA方法具有更好的性能。
Generalized discriminant analysis (GDA) is an extension of the classical linear discriminant analysis (LDA) from linear domain to a nonlinear domain via the kernel trick. However, in the previous algorithm of GDA, the solutions may suffer from the degenerate eigenvalue problem (i.e., several eigenvectors with the same eigenvalue), which makes them not optimal in terms of the discriminant ability. In this letter, we propose a modified algorithm for GDA (MGDA) to solve this problem. The MGDA method aims to remove the degeneracy of GDA and find the optimal discriminant solutions, which maximize the between-class scatter in the subspace spanned by the degenerate eigenvectors of GDA. Theoretical analysis and experimental results on the ORL face database show that the MGDA method achieves better performance than the GDA method.