From K-means we know that:
- K-means forces clusters to be spherical
- In K-means clustering every point can only belong to one cluster
But sometimes it might be desirable to have elliptical clusters than spherical clusters. And what if there is a data point right in the center of two clusters?
Gaußian Mixture Model
With a random variable , the mixed Gaussian model can be expressed by:
where is the component of the mixture model.
Then we can generate a generalized form:
Now the goal for the algorithm is: given , determine the parameters , and (for example by maximizing the likelihood)
Model Iteration Illustration