[Mixture Models] EM Algorithm
[Mixture Models] EM Algorithm

Maximizing likelihood could not be used to the Gaussian mixture model directly, for its severe defects that we have come across at 'Maximum Likelihood of Gaussian Mixtures'. By the inspiration of K-means, a two-step algorithm was developed.

[Mixture Models] Mixtures of Gaussians
[Mixture Models] Mixtures of Gaussians

We have introduced a mixture distribution in the post 'An Introduction to Mixture Models'. And the example in that post was just two components Gaussian Mixture. However, in this post, we would like to talk about Gaussian mixtures formally. And it severs to motivate the expectation-maximization(EM) algorithm.

[Mixture Models] K-means Clustering
[Mixture Models] K-means Clustering

Original form K-Means algorithm might be one of the most accessible algorithms in machine learning. And many books and courses started with it. However, if we convert the task which K-means dealt with into a more mathematical form, there would be more interesting aspects coming to us.