Regularized Unilateral Two-dimensional Linear Discriminant Analysis

The idea of discriminant analysis is to use some known research methods to determine the group to which a new observation sample belongs after dividing the target research object into several groups under certain number of samples.Discriminant analysis is also one of the dimensionality reduction methods in data preprocessing.It is a supervised classification.The main task of discriminant analysis is to extract the features that are most conducive to classification and use this space for classification.In addition,this paper considers the feature extraction based on the vector as a onedimensional method and the feature extraction based on the matrix as a twodimensional method.The one-dimensional method,such as LDA,aims to determine how to get the extreme value of the Fisher criterion function,and the vector that takes this extreme value is the best projection direction.This will change the projection of the sample in this optimal projection direction,so that it has the largest inter-class dispersion and the smallest intra-class dispersion.Two-dimensional methods such as 2DLDA are an extension of LDA's processing of matrix data.The most prominent advantage of 2DLDA is that it does not need to consider how to convert highdimensional matrix data into vectors,so it can achieve the goal of reducing our calculation amount.At the same time,part of the discriminant analysis algorithm introduced by the regularization process has also been continuously developed and improved,and it takes new information into consideration to make new estimates.However,both the existing unilateral two-dimensional discriminant analysis and regularized discriminant analysis have defects such as higher-dimensional inter-class and intra-class dispersion matrices and larger feature dimensions.In order to further improve feature extraction,Efficient and accurate,so by extending the regularized linear discriminant analysis to the unilateral two-dimensional linear discriminant analysis,a regularized unilateral two-dimensional linear discriminant analysis(R2DLDA)is obtained.The main research method is to add a regularization process based on unilateral two-dimensional linear discriminant analysis.The regularization process determines the optimal regularization parameter by cross-validation,and then finds the best projection matrix to judge the classification effect.In the following article,in order to verify the discriminative classification performance of R2 DLDA,consider verifying with data,that is,five real data sets are selected,experiments are designed,and experiments are performed on these data sets.Through experiments and the corresponding dimensionality reduction results and classification error rates,compared with 2DLDA and 2DPCA,it is confirmed that R2 DLDA is superior in classification accuracy and dimensionality reduction effect.