What is “mixture” in a gaussian mixture model

We often study Gaussian Mixture model as a useful model in machine learning and its applications.

What is the physical significance of this “Mixture“?

Is it used because a Gaussian Mixture Model models the probability of a number of random variables each with its own value of mean? If not, then what is the correct interpretation of this word.

A distribution combines different component distributions with weights that typically sum to one (or can be renormalized). A is the special case where the components are Gaussians.

For instance, here is a mixture of 25% $N(-2,1)$ and 75% $N(2,1)$, which you could call “one part $N(-2,1)$ and three parts $N(2,1)$“:

xx <- seq(-5,5,by=.01)
plot(xx,0.25*dnorm(xx,-2,1)+0.75*dnorm(xx,2,1),type="l",xlab="",ylab="")

Essentially, it’s like a recipe. Play around a little with the weights, the means and the variances to see what happens, or look at the two tags on CV.