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The Regularization Algorithm Based on Least Squares Linear Discriminant Analysis

LIU Zun-xiong,ZENG Li-hui(School of Information Engineering,East China Jiaotong University,Nanchang 330013,China)  
Linear Discriminant Analysis(LDA) is a well-known technique for dimensionality reduction and classi fication,while the classical LDA formulation fails when the total scatter matrix is singular,encountered usually in un dersampled problems.In this paper,regularized Least Squares LDA(RLS-LDA) based on L2-norm,L1-norm and the elastic net,is proposed to handle the problems,the resulting models are robust and sparse.Firstly,the theories about linear regression and regularization are explored,and the equivalence relationship between the least squares formulation and LDA for multi-class classifications under a mild condition is summarized.Secondly,the construction of RLS-LDA is presented.Performance evaluations of these approaches are conducted on benchmark collection of text documents.Results demonstrate the effectiveness of the proposed RLS-LDA and it’s the RLS-LDA based on the elastic net that is better than others.
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