【Machine Learning】K-means clustering algorithm and EM algorithm

　　1、The step of K-means clustering algorithm :

　　Step 1: Initialize cluster centroids  randomly

　　Step 2: Repeat until convergence:{

　　　　　　　　For every i, set

　　　　　　　　　　　　　　 

　　　　　　　　For every j, set

　　　　　　　　　　　　　　

　　　　　　　　}

　　Definition:  are the training data set.

　　Analysis: K(a parameter of the algorithm)is the number of clusters.First, we get K cluster centorids, then, we iterate through each data point  ，to find the closest cluster centroid  , next, moving each cluster centroid  to the mean of the points assigned to it. Repeat last two step until convergence.

　　K-means algorithm is used to find local optimal solution. The initialization can significantly affect the result of clustering.

　　2、EM(Exceptation-Maximization) algorithm