## Background

To get strong understanding about EM concept, digging from the mathematical derivation is good way for it. But before it, let’s put the condition first. EM method is intended for clustering, and the most familiar method is k-means clustering, which is the special case of EM method that use Gaussian mixture to model the cluster areas and using hard clustering instead of soft clustering.

See picture below.

Picture above shows that we have 4 clusters where each cluster is modeled using Gaussian. To determine the data belongs to which cluster, we can just determine by finding the maximal value among the fourth Gaussian value. The data will be clustered to the cluster whose Gaussian value is maximal in that location. For instance, the area in the pink line boundary has maximal Gaussian value which is from Gaussian value in cluster 1, likewise for other clusters. Doing this type of clustering, the clustering boundary may intersects each others and taking cluster whose the value is maximal, is called soft clustering. Whereas for hard clustering, the boundary doesn’t intersect each others. To be able to cluster like that, we need parameters mean and variance of all those 4 Gaussian distributions, given data set input without class label. And we can achieve this by using EM method. Continue reading “How EM (Expectation Maximization) Method Works for Clustering”