# Gaussian Mixture Models + EM algorithm - Videos

Here are some good slides about the GMM+EM topic:

Below you find also some helpful videos to understand the topic from scratch.

## EM

The EM algorithm has a simple basic idea.

Consider e.g. you observe some data points {x_1, …, x_N} that stem from 2 Gaussians.

But you do not know the parameters of theses Gaussians: their means and covariance matrices and the probability that a data point stems from the 1st or the 2nd Gaussian. These parameters are unobservable, hidden, or “latent”.

EM can find good values for these latent variables by an iterative procedure.

Starting with some initial guess for these parameters we first

• estimate the probability for each data point that it comes from the 1st or 2nd Gaussian (E-step)
• then use this assignment of datapoints to the Gaussians to update the estimates for the latent variables, i.e. the means, covariance matrices, and “data point producer probabilities” (M-step)

To sum it up:

Expectation-maximization, as expected, works in two alternating steps. Expectation refers to computing the probability that each datum is a member of each class; maximization refers to altering the parameters of each class to maximize those probabilities.
from jormungand.net

### EM explanation #1

Easy & very fast explained:

### EM explanation #2

Explanations by Andrew Ng from Stanford University (start at minute 18):

### EM explanation #3

A little bit more general explained: