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具有统计不相关性的最佳鉴别特征空间的维数定理 被引量:9

A Theorem on Dimensionality of the Uncorrelated Optimal Discriminant Feature Space
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摘要 提出并严格证明了具有统计不相关性的最佳鉴别特征空间的维数定理 :对含有L个类别的模式识别问题 ,具有统计不相关性的最佳鉴别特征空间的维数为 (L - 1) ;说明了具有统计不相关性的最佳鉴别变换与Wilks所提出的经典的模式特征抽取方法的关系 .在一定的条件下 ,具有统计不相关性的最佳鉴别矢量集等价于Wilks所提出的经典鉴别矢量集 .经典的模式特征抽取方法可以用来在不损失任何Fisher鉴别信息的意义下 ,对含有L个类别的模式识别问题 ,抽取 (L - 1) Based on Fisher's discriminant criterion function, optimal sets of discriminant vectors has great influence in the area of pattern recognition. The uncorrelated optimal discriminant transformation had been proposed by the authors of this paper. Experiments on Concordia University CENPARMI handwritten numeral database and ORL face database showed that when the number of training samples is large, the conjugate orthogonal set of optimal discriminant vectors can be much more powerful than the orthogonal set of optimal discriminant vectors and the uncorrelated optimal discriminant transformation is superior to the existing Foley Sammon optimal discriminant transformation. This paper presents and demonstrates a theorem on dimensionality of the uncorrelated optimal discriminant feature space. It is claimed that for L class problems, the dimensionality of the uncorrelated optimal discriminant feature space is ( L-1 ). This paper discusses the relationship between the uncorrelated optimal discriminant transformation and the existing classical feature extraction method proposed by Wilks. From the theorem proposed in this paper, the classical optimal discriminant vectors proposed by Wilks are equivalent to the uncorrelated optimal discriminant vectors, and can be used to extract (L-1 ) uncorrelated optimal discriminant features for L class problems without losing any discriminant information in the meaning of Fisher's discriminant criterion function.
出处 《计算机学报》 EI CSCD 北大核心 2003年第1期110-115,共6页 Chinese Journal of Computers
基金 国家自然科学基金 ( 60 0 72 0 3 4)资助
关键词 统计不相关性 最佳鉴别特征空间 维数定理 图像特征 模式识别 pattern recognition feature extraction discriminant analysis dimension problem
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参考文献8

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同被引文献67

  • 1陈绵书,陈贺新,刘伟.一种新的求解无相关鉴别矢量集方法[J].计算机学报,2004,27(7):913-917. 被引量:10
  • 2吴小俊,杨静宇,王士同,Josef Kittler.广义统计不相关最优鉴别矢量集的一个理论结果[J].电子学报,2004,32(10):1720-1722. 被引量:4
  • 3吴小俊,杨静宇,王士同,Josef Kittler,陆介平.改进的统计不相关最优鉴别矢量集[J].电子与信息学报,2005,27(1):47-50. 被引量:8
  • 4刘华林,杨万麟.基于QR分解的广义辨别分析用于雷达目标识别[J].红外与毫米波学报,2007,26(3):205-208. 被引量:4
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  • 7Yang Jian, Zhang David, Xa Yong, et al. Two-dimensional diseriminant transform for face recognition [ J ]. Pattern Recognition,2005,38 ( 7 ) : 1125-1129.
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  • 10Jin Zhong, Yang Jing-yu, Tang Zhen-min, et al. A theorem on uncorrelated optimal discriminant vectors, Pattern Recognition, 2001,34(10) : 2041-2047.

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