Ayoub, it is a standard excercise to show that a covariance matrix is always symmetric and positive definite (just google "covariance positive definite proof"). Hence all eigenvalues are positive and thus the determinant is also positive.

I assume you must have done a mistake when calculating the determinant (some indexes shifted wrongley etc.). If not - did you look at the largest and smallest eigenvalue of your covariance matrix yet? Maybe your problem is ill-conditioned and a small positive eigenvalue turns into a small negative eigenvalue due to numerical problems... In which case you might need to regularize the matrix to bound the eigenvalues away from 0. I had a similar problem a couple of weeks ago. It turned out that I messed up the indexing of the matrix elements and the covariance matrix was therefore not symmetric anymore. Good luck!

Unfortunately, the problem of ill-conditioned covariance matrices is a common problem in GMM training. That is the reason why the most of speech/speaker recognition systems use diagonal covariances only. Even the variances can be close to zero (with some numerical luck even negative)...

I have a Matlab implementation of robust GMM training a specially suited for speech data.

Thank you very much Dear Jan Vanek for your response ... can you give me the implementation that you developed ?? ... My E-mail is : [email protected]

Thank you in advance.

Covariance matrix is always positive semi definite. That means the determinant must be >=0. When you have it equals to zero, that mean the matrix is rank deficient. Theoretically it cannot be negative but in numerical calculation, numerical roundoff error causes it to become negative sometime. But the magnitude of this negative value should be very small. If you get large negative value, then your method of calculation of determinant is wrong.

dear Jan Vanek, I am interested to get the implementation you have developed. My email is [email protected]

Thank you very much!

The contents of my covariance matrix are negative like

0.0020 -0.0010 -0.0006

-0.0010 0.0020 0.0006

-0.0006 0.0006 0.0053

but deteminant is positive ,near to zero....Is there any problem?

Dear Ibrahim,

when the covariance is positive, It means that when one variable increases the other one is increases.when it is negative, the direction of changes are reverese.e.g. one increases, the other one decreases. i think contrivance does not effect on determinant. it is also a symmetric matrix and symmetric matrix always has +ve determinant.  

Why is it that my covariance matrix in Kalman filter is not symmetric and positive definite

Hello Jan Vanek ,

I'm interested in the Matlab implementation of robust GMM training that you have developed. Can you share it with me on [email protected]?

Thank you very much!

Regards,

Sayali Kedari

Dear Jan Vanek,

Please can you share your Matlab implementation of robust GMM via [email protected]

Best of thanks

Dear Jan Vanek,

I was wondering if you could please send me your implementation of the robust GMM. My email address is [email protected].

Thanks in advance!