CODEWITHSUNDEEP
matlabdistribution
com
com

Reputation: 2704

matlap GMM of multivariate distibutions

I am a newbie in Matlab, so sorry for a stupid question.

I want to create a sequence of 2-dimensional vectors generated from GMM that consist of three multivariate normal distributions.

so, let's start

 mu = [[0 1]; [0 2]; [0 3]]
 cov = cat(4, 0, 0.5)
 p = [0.4 0.4 0.2]
 obj = gmdistribution(mu, cov, p)

The problem is this sequence of commands doesn't work.

In addition, I want these three distribution to have a small overlap. I don't know how to evaluate mu and cov such that they will have a small overlap.

Upvotes: 0

Views: 105

Answers (1)

hbaderts
hbaderts

Reputation: 14316

First, cov is the name of the covariance function, so you better call your variable e.g. sigma. Second, you create the cov variable to be a 4-D array with value 0 at cov(1,1,1,1) and 0.5 at cov(1,1,1,2).

Depending on how the covariance matrices looks, the variable sigma can look different. Let d be the number of dimensions (2 in your example), and k be the number of distributions (3 in your example).

General case: Each of the Gaussian distributions has an arbitrary covariance matrix. sigma is of size dxdxn, i.e. 2x2x3, where sigma(:,:,k) is the kth covariance matrix. Note that of course the covariance matrices have to be symmetric and positive semidefinite. You do that e.g. by

sigma(:,:,1) = [1.0, 0.5 ; 0.5, 2.0];
sigma(:,:,2) = [0.8, 0.1 ; 0.1, 0.2];
sigma(:,:,3) = [1.2, 0.4 ; 0.4, 0.3];

Diagonal covariance matrices If all your covariance matrices are diagonal, you can specify sigma as a 1xdxk(1x2x3) matrix, where sigma(1,:,k) are the diagonal elements of the kth covariance matrix. E.g.

sigma(1,:,1) = [1.0, 2.0];
sigma(1,:,2) = [0.8, 0.2];
sigma(1,:,3) = [1.2, 0.3];

Identical covariance matrices If all k covariance matrices are identical, it is enough if you specify it once

sigma = [1.0, 0.5 ; 0.5, 2.0];

Identical, diagonal covariance matrices If all k covariance matrices are identical diagonal matrices, sigma is a vector containing the diagonal elements

sigma = [1.0, 2.0];

Upvotes: 1

Related Questions