Mahalanobis距离在多元随机变量线性变换中的定理

Theorem of Mahalanobis Distance from Multivariate Random Variables Linear Transformation

根据多元统计分析中Mahalanobis距离的计算理论,对其计算性质进行了讨论和研究,证明了多元随机变量在经过可逆线性变换后,其Mahalanobis距离的计算数值不变这一重要性质.并通过实际问题说明了此性质在多元统计分析,特别是在距离判别分析中的作用.

According to multivariate statistical analysis of the calculation theory of Mahalanobis distance, the nature of its calculation were discussed and studied. It has proved an important nature that the numerical calculation of Mahalanobis distance of multivariate random variables is unchanged after the reversible linear transformation. And it has illustrate through the example that the nature has an effect on multivariate statistical analysis, especially on distance discriminant analysis.