why, if I have data highly correlated, i obtain Ill-conditioned covariance when i use fitgmdist?

GMModel_Sani = gmdistribution.fit(Matrice_Training_Sani,2);
GMModel_Malati = gmdistribution.fit(Matrice_Training_Malati,2);

Answer 1

[Roger Stafford]

Just suppose that the correlation between each pair is one. Then the correlation matrix would consist of all ones and such a matrix is certainly ill-conditioned, since its determinant is zero. The covariance matrix in such a case would also have a zero determinant and therefore be singular, since it is obtained from the correlation matrix by multiplying rows and columns by the standard deviation values, and that just multiplies the determinant by these std values. With strong correlation you will begin to approach this condition.