Is there any solution to make positive semi-definite covariance matrix?

I have image data. row of the data represents pixel and column represents rgb values. that is, the size of the data is N by 3. However, I would like to apply kmeans and GMM for clustering. But the covariance matrix is not positive semi-definite.

Why and what is solution?

Answer 1

[Walter Roberson]

Covariance matrices of real variables are always positive semi-definite. See http://math.stackexchange.com/questions/114072/what-is-the-proof-that-covariance-matrices-are-always-semi-definite

If you calculated a covariance matrix but it is being reported as not positive semi-definite then you might have encountered numeric round-off. In such a case use

(X.' + X) / 2

in place of X: this will eliminate any round-off error that is keeping the matrix from being completely symmetric.

[K M Ibrahim Khalilullah]

Thank you very much for your answer. would you tell me about X please? is the X data or covariance matrix?

[Walter Roberson]

The covariance matrix