dm.cs.tu-dortmund.de/en/mlbits/cluster-em-intro/
Gaussian Mixture Modeling Introduction – Lecture Notes
w_1, \mu_2, \Sigma_2, w_2, \ldots \mu_k, \Sigma_k, w_k)\]
expect cluster labels based on Gaussian distribution density
update Gaussian models with the mean, covariance matrix, and weight
repeat (2.)–(3.) [...] E-step, and the M-step.
For Gaussian Mixture modeling, \(\smash {\theta =(\mu_1,\Sigma_1,w_1,\mu_2,\Sigma_2,w_2, \ldots , \mu_k,\Sigma_k,w_k)}\)
In contrast to \(k\) -means, we need to use a stopping threshold [...] \[\operatorname {pdf}(p,\mu ,\Sigma ) = \frac{1}{\sqrt{\rule{0pt}{9pt}\smash {(2\pi )^d |\Sigma |}}} \cdot e^{-\frac{1}{2} \big((p-\mu )^T\Sigma ^{-1}(p-\mu ) \big)}\]
If we constrain \(\Sigma\) we can …
