# What is the general form of EM algorithm?

## What is the general form of EM algorithm?

The EM algorithm is an iterative approach that cycles between two modes. The first mode attempts to estimate the missing or latent variables, called the estimation-step or E-step. The second mode attempts to optimize the parameters of the model to best explain the data, called the maximization-step or M-step.

What is EM clustering algorithm?

The EM algorithm extends this basic approach to clustering in two important ways: Instead of assigning examples to clusters to maximize the differences in means for continuous variables, the EM clustering algorithm computes probabilities of cluster memberships based on one or more probability distributions.

What is EM in NLP?

Expectation Maximization (EM) is a classic algorithm developed in the 60s and 70s with diverse applications. It can be used as an unsupervised clustering algorithm and extends to NLP applications like Latent Dirichlet Allocation¹, the Baum–Welch algorithm for Hidden Markov Models, and medical imaging.

### How to summarize the process of EM algorithm?

From this update, we can summary the process of EM algorithm as the following E step and M step. Let’s take a 2-dimension Gaussian Mixture Model as an example. Here, if an observed data x is generated from m-th Gaussian distribution, then z_m = 1, else z_m = 0.

Does the EM algorithm fall into local optimal state?

However, since the EM algorithm is an iterative calculation, it easily falls into local optimal state. As saw in the result (1), (2) differences in M value (number of mixture model) and initializations offer different changes in Log-likelihood convergence and estimate distribution.

Does the EM algorithm always converge the log-likelihood function?

From the result, with the EM algorithm, the log-likelihood function always converged after repeat the update rules on parameters. However, since the EM algorithm is an iterative calculation, it easily falls into local optimal state.