Before we discuss Gaussian Mixture Models (GMMs), let's understand what Mixture Models are. A Mixture Model is a type of probability density model where we assume that the data is governed by a number of component distributions. If these distributions are Gaussian, then the model becomes a Gaussian Mixture Model. These component distributions are combined in order to provide a multi-modal density function, which becomes a mixture model.

Let's look at an example to understand how Mixture Models work. We want to model the shopping habits of all the people in South America. One way to do it would be model the whole continent and fit everything into a single model. But we know that people in different countries shop differently. We need to understand how people in individual countries shop and how they behave.

If we want to get a good representative model, we need to account for all the variations within the continent. In this case, we can use mixture models...