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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?

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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.

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