# Questions revolving GMM & EM

I am currently reading about the guassian mixture model and the expectation–maximization algorithm. From what I am reading the two differences between the two here is what I've come up with so far, are they correct?

• GMM is a model, it's a way to represent the data (subpopulations of the entire population)
• EM is an algorithm, it is a process to represent a specific model (GMM in this case)

My final question is, let's say you have a population, I've been reading that you must define k (amount of clusters) before using an algorithm (EM in this case). Is this related to supervised vs. unsupervised algorithms? In other words, in supervised algorithms you define how many clusters there are in advance and train the cluster, while unsupervised would calculate the amount of clusters it's own. Is this the reason why you must define k?

• Supervised v Unsupervised has to do with whether the algorithm uses training data that is labeled or not, respectively. You're correct that specifying or learning K has a supervised or unsupervised flavor to it, but that application of the terms would be non-standard and misleading. Dec 2, 2014 at 16:00

That you have to define $k$ before using EM is not itself to do with supervised/unsupervisedness. AFAIK it is to do with the fact that the standard EM algorithm supposes you know the structure of the model / what parameters are involved.
By way of contrast, you can have non-parametric clustering algorithms for regression. I.e. where you do not specify $k$, and both the number of clusters and cluster assignments are learnt from the data. Other algorithms are used for inference in such models e.g. MCMC.
• More like 'you must guess $k$ if you want to use EM to fit the mixture'. Where guess might involve something like getting the AIC for a bunch of different $k$, then going with the best one. If you don't want to guess $k$ one way of proceeding is to do a Bayesian Dirichlet Process mixture model with fitting/inference done via MCMC. Dec 2, 2014 at 16:20