关键词: 分类, 高维数据, 随机矩阵理论, 线性判别分析, 协方差矩阵

Abstract: Linear discriminant analysis (LDA) is an important theoretical and analytic tool for many machine learning and data mining tasks.As a parametric classification method,it performs well in many applications.However,LDA is impractical for high-dimensional data sets which are now routinely generated everywhere in modern society.A primary reason for the inefficiency of LDA for high-dimensional data is that the sample covariance matrix is no longer a good estimator of the population covariance matrix when the dimension of feature vector is close to or even larger than the sample size.Therefore,this paper proposed a high-dimensional data classifier regularization method based on random matrix theory.Firstly,a truly consistent estimation was conducted for high-dimensional covariance matrix through rotation invariance estimation and eigenvalue interception.Secondely,the estimated high-dimensional covariance matrix was used to calculate the discrimination function value.Numerical experiments on the artificial datasets,as well as some real world datasets such as the microarray datasets,demonstrate that the proposed discriminant analysis method has wider applications and yields higher accuracies than existing competitors.

Key words: Classification, Covariance matrix, High-dimensional data, Linear discriminant analysis, Random matrix theory