The EM algorithm is a statistical algorithm that finds the maximum likelihood parameter. Since it supports soft cluster assignment, assuming that the mixed Gaussian distribution that generates samples and data can be assigned to multiple clusters at the same time with some degree of confidence, you will find that the algorithm is a general version of K-means clustering. The mixed Gaussian distribution that's generating the data is a weighted sum of the Gaussian distribution function:
Each Gaussian distribution has 
as its mean and 
as its covariance matrix. 
represents the weight on the kth distribution for this sample. Now, let's introduce a hidden parameter to express the cluster assignment. Here, we will use 
. z is a one-k-encoded vector. The data is assigned to the kth cluster, the kth element has a z of 1, while the other...
