4. General EM for GMMPermalink
In this part, we’ll see how EM algorithm can be applied in GMM.
It will be as the below.
E stepPermalink
M stepPermalink
- EM : Update parameters to maximize
- GMM : Update Gaussian parameters to fit points assigned to them
We’ll see how the equation became like the above.
M-step for GMMPermalink
Let’s take an example when t_i = 1,2,3 ( a total of three clusters(Gaussians) )
[ optimize for ‘mu’ ]Permalink
Let’s optimize the expression above with respect to mu_1.
If we multiply it by sigma_1 ( = variance of the first gaussian ) and the solve the equation, the result will be like this.
[ optimize for ‘sigma’ ]Permalink
This time, let’s optimize the expression above with respect to sigma_c. Like the same way as the above, the result will
be like this.