I have D-dimensional data with K components. How many parameters if I use a model with full covariance matrices? and How many if I use diaogonal covariance matrices?


1 Answer 1


Simply do the math.

For each Gaussian you have:
1. A Symmetric full DxD covariance matrix giving (D*D - D)/2 + D parameters ((D*D - D)/2 is the number of off-diagonal elements and D is the number of diagonal elements)
2. A D dimensional mean vector giving D parameters
3. A mixing weight giving another parameter

This results in Df = (D*D - D)/2 + 2D + 1 for each gaussian.
Given you have K components, you have (K*Df)-1 parameters. Because the mixing weights must sum to 1, you only need to find K-1 of them. The Kth weight can be calculated by subtracting the sum of the (K-1) weights from 1.

In the diagonal case the covariance matrix parameters reduce to D, because of the abscence of off-diagonal elements.
Thus yielding Df = 2D + 1.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.