Model-based finite mixtures using the EM algorithm. This uses relative differences between log-likelihoods
to check for convergence. If the estimated covariance matrices become close to singular, the function returns
empty arrays for the model.
DATA is a matrix of observations, one on each row.
The following are the initial values to start the EM algorithm:
MUIN is an array of means, each column corresponding to a mean.
VARIN is a vector of variances in the univariate case. In the
multivariate case, it is a 3-D array of covariance matrix, one
page per component density.
WTSIN is a vector of weights.
MODEL is one of the following models:
SPHERICAL FAMILY (DIAGONAL COVARIANCE, SAME VARIANCES FOR VARIABLES/DIMENSIONS):
1. COV are of form lambda*I (clusters have equal covariances)
2: COV are of form lambda_k*I (clusers have unequal covariances)
DIAGONAL FAMILY (DIAGONAL COVARIANCE, DIFFERENT VARIANCES FOR VARIABLES/DIMENSIONS):
3. COV are of form lambda*B (clusters have equal covariances)
4. COV are of form lambda*B_k (clusters have same volume, unequal shape)
5. COV are of form lambda_k*B_k (clusters have unequal volume, unequal shape)
where B = diag(b_1,...,b_d); B is a diagonal matrix with different values and
det(B) = 1.
GENERAL FAMILY (FULL COVARIANCE, OFF-DIAGONAL ELEMENTS ARE NON-ZERO)
6. COV are of form lambda*D*A*D' (clusters have equal covariance)
7. COV are of form lambda*D_k*A*(D_k)' (clusters have different orientation)
8. COV are of form lambda*D_k*A_k*(D_k)' (clusters have different orientation and shape)
9. COV are of form SIGMA_k_hat (unconstrained, all aspects vary)
where lambda represents the volume, D governs the orientation, and A is a diagonal matrix
that describes the shape.
[WTS,MUS,VARS] = MBCFINMIX(DATA,MUIN,VARIN,WTSIN,MODEL)
Model-Based Clustering Toolbox documentation.
Model-Based Clustering homepage.