监督降维算法的计算和理论分析.pdf

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2 rvised dimensionality reduction. Journal of Zhejiang University ( Science
Edition) , 2009 ,36 (6) :670 - 674
Abstract : In the case of small sample size , classical linear discriminant analysis fails due to the singularity of scatter
matrices for supervised dimensionality reduction. Many extensions were proposed in the past to overcome this
problem , which in general can be classified into three categories : methods based on the null space of the within class
scatter matrix , ones based on the range space of the total scatter matrix and ones based on other subspace. In order
to better understand the characteristics of the algorithms of the former two classes , a computational and theoretical
analysis was carried out , and concluded that : under a mild condition which holds in many applications involving
high dimensional data , methods based on the null space of the within class scatter matrix are equivalent to those
based on the range space of the total scatter matrix except two differences of constraints for discriminant vectors and
implementation procedure. The comparative results on the face database , ORL and YAL E , also confirmed the
aforementioned conclusion.
Key Words : generali