Mahalanobisavstander
Mahalanobisavstander, or Mahalanobis distances, are a multivariate measure of the distance between a point and a distribution. They account for the correlations among variables and the scale of each variable, providing a geometry that reflects the data structure rather than mere coordinate differences. The concept is named after Indian statistician Prasanta Chandra Mahalanobis, who introduced it in 1936 to identify multivariate outliers and compare observations across different populations.
For a vector x in R^p, with mean vector μ and covariance matrix Σ, the squared Mahalanobis distance
Key properties include affine invariance under linear transformations and an interpretation in terms of ellipsoidal contours:
Applications span outlier detection, cluster analysis, classification, and finance, where understanding joint variability is important. Limitations