# Elbow Test using AIC/BIC for identifying number of clusters using GMM

How to select number of clusters using GMM when the elbow test (AIC/BIC vs n_components) results in a graph like this?

• 6 seems to be what you are looking for, if you are looking for a test there are a few, for ex. using clusGap statistic. – user2974951 Sep 25 '18 at 8:51

This plot shows how the AIC and BIC change as a function of the number of clusters. While the AIC continuous to decrease with a larger number of clusters, you can see that the BIC stops decreasing after $$k=6$$ clusters. For this reason, you could choose $$k = 6$$.
Another way to choose the 'best' number of clusters is by considering the elbow(s) of the figure. The elbow of a function is a point after which the decrease becomes notably smaller. An elbow is a heuristic, so there is no exact way to determine which value best describes this point. For example, one could argue that the AIC & BIC both stop decreasing as much after $$k = 5$$ clusters, while someone else might argue that this is after $$k = 6$$ clusters. You could even argue that the biggest decrease has already happened after $$k = 2$$ clusters.
Lastly, you don't have to choose any number of clusters just because AIC/BIC/whatever suggested you do so. If you have some a priori reason to assume that there should be $$k = 3$$ clusters, then that might be a better choice.