Mahalanobis Distance(马氏距离)

http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_covariance_matrix.htm马氏距离

对normalized Euclidean distance的扩展。

两种特殊情况：

一：如果是单位矩阵

If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance.

 

二：如果是协方差矩阵式对角矩阵

If the covariance matrix is diagonal, then the resulting distance measure is called the normalized Euclidean distance

广泛使用：

Mahalanobis distance is widely used in cluster analysis and other classification techniques. It is closely related to Hotelling's T-square distribution used for multivariate statistical testing and Fisher's Linear Discriminant Analysis that is used for supervised classification.^[6]

 

^协方差

 

http://www.aiaccess.net/English/Glossaries/GlosMod/e_gm_covariance_matrix.htm