多变量统计分析中独立变量数目的判定方法

数据空间的不均匀性是导致基于样本协方差矩阵特征值的多变量系统独立变量数目判定误差的原因.为此,文中提出了一种多变量统计分析中独立变量数目的判定方法.该方法首先对样本数据马氏距离化,然后添加均匀白噪声以掩蔽数据空间的不均匀性,最后降序排列协方差矩阵的特征值,计算对数值,并求二阶差分,所得序列值分为与零值有微小差异的噪声贡献和与零值有明显差异的独立变量贡献,从而实现了独立变量数目的准确判定.算例和实验结果均表明,该方法判定结果准确、清晰、稳定.

Determination of Independent Variable Number in Multi-Variable Statistical Analysis

In the multi-variable system,there generally exist errors in the determination of independent variable number based on covariance matrix eigenvalues because of the nonuniformity in data space.To solve this problem,a method is proposed to determine the independent variable number in multi-variable statistical analysis.In this method,sample data are first changed in Mahalanobis distance,and are then added with uniform white noise to shield the nonuniformity in data space.After the processing with uniform white noise,by arraying the covariance matrix eigenvalues in descending order and calculating the eigenvalues logarithm,the second difference is obtained.So,a successive value is deduced,which is divided distinctly into two parts,one is related to the noise that is almost equal to zero,and the other is related to the independent variables that are obviously different from zero,ma-king the independent variable number accurately determined.The simulation example and the experiments all reveal that the proposed method is exact,distinct and steady.