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