Statistics Toolbox

mahal

Mahalanobis distance

Syntax

• d = mahal(Y,X)
  

Description

mahal(Y,X) computes the Mahalanobis distance of each point (row) of the matrix Y from the sample in the matrix X.

The number of columns of Y must equal the number of columns in X, but the number of rows may differ. The number of rows in X must exceed the number of columns.

The Mahalanobis distance is a multivariate measure of the separation of a data set from a point in space. It is the criterion minimized in linear discriminant analysis.

Example

The Mahalanobis distance of a matrix r when applied to itself is a way to find outliers.

• r = mvnrnd([0 0],[1 0.9;0.9 1],100);
  r = [r;10 10];
  d = mahal(r,r);
  last6 = d(96:101)
  
  last6 =
  
      1.1036
      2.2353
      2.0219
      0.3876
      1.5571
     52.7381
  

The last element is clearly an outlier.

See Also
classify

mad

manova1