# GMM - Covariance matrix is causing exponential to tend to infinity

We are trying to create a GMM that can recognise targets in a picture and pick them out. We have got to the point when the system can identify features in the image and test them against a GMM, however I think the covariance matrix is incorrect. One of my questions is whether a Covariance Matrix has to meet certain other mathematical rules such as being symetrical but I'm not sure what else. Here is the Covariance matrix made by our software:

Covariance Matrix

With a mean vector of

Mean Vector

I have checked the feature vector that we use creates these using matlab.

However when we attempt to calculate the provbablitly of an image belgoing to the model usign the standard equation it tends to infinity as a result of the exponential being raised to a extremly high power.

The Features that we use are not the best and may be the source of the issue. The training images are just circular tarbets.

The current features that we use are: - The black white ratio - White pixels on the Diagonal (right) - White pixels on the Diagonal (left) - White pixels on the Vertical - White pixels on the Horizontal - Width - Height

We have tried using histograms to extract other features but this had the same problem.

The covariance matrix must be positive semi-definite. Equivalently, all eigenvalues must be $\ge 0$. When I calculated the eigenvalues of your matrix, one was negative, so it's not a valid covariance.