Statistics Toolbox™

mahal - Mahalanobis distance to component means

Class

@gmdistribution

Syntax

D = mahal(obj,X)

Description

D = mahal(obj,X) computes the Mahalanobis distance (in squared units) of each observation in X to the mean of each of the k components of the Gaussian mixture distribution defined by obj. obj is an object created by gmdistribution or fit. X is an n-by-d matrix, where n is the number of observations and d is the dimension of the data. D is n-by-k, with D(I,J) the distance of observation I from the mean of component J.

Example

Generate data from a mixture of two bivariate Gaussian distributions using the mvnrnd function:

MU1 = [1 2];
SIGMA1 = [2 0; 0 .5];
MU2 = [-3 -5];
SIGMA2 = [1 0; 0 1];
X = [mvnrnd(MU1,SIGMA1,1000);mvnrnd(MU2,SIGMA2,1000)];

scatter(X(:,1),X(:,2),10,'.')
hold on

Fit a two-component Gaussian mixture model:

obj = gmdistribution.fit(X,2);
h = ezcontour(@(x,y)pdf(obj,[x y]),[-8 6],[-8 6]);

Compute the Mahalanobis distance of each point in X to the mean of each component of obj:

D = mahal(obj,X);

delete(h)
scatter(X(:,1),X(:,2),10,D(:,1),'.')
hb = colorbar;
ylabel(hb,'Mahalanobis Distance to Component 1')

See Also

gmdistribution, cluster, posterior, mahal

mahal

maineffectsplot