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?
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
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.
Df = 2D + 1.