MATLAB: Combine two or more gaussian components into one Gaussian Mixture (gmdistribution)

gaussian mixturegmdistribution

Hello,
Is there any way to combine two (or more) separate Gaussian Components into one?
clear; close all; clc;
N = 25; % N-points
D = 2; % D-dimensions
% generate data 
X = randn(N,D);
Y = randn(N,D)+2; % +2 to spatially separate data components
% model gaussian components
muX = mean(X,1)
SX = cov(X)
muY = mean(Y,1)
SY = cov(Y)
GX = gmdistribution(muX,SX,1) % first component
GY = gmdistribution(muY,SY,1) % second component
% COMBINE !
GC = ???????????????(GX,GY);
I would like to get output like this:
GC = 
    Gaussian mixture distribution with 2 components in 2 dimensions
    Component 1:
    Mixing proportion: 0.500000
    Mean:   -0.0017   -0.1167
    
    Component 2:
    Mixing proportion: 0.500000
    Mean:   -0.0037   0.1367

Best Answer

Doesn't
GC = gmdistribution( [muX; muY], cat( 3, SX, SY ), [1; 1] );
work?
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