Perhaps the most widely used clustering family of algorithms is k-means. In this section, we will examine how it works and ways to assess the quality of a clustering solution.
K-means is a partitioning algorithm that produces k (user-defined number) clusters of cases that are more similar to each other than to cases outside the cluster. K-means starts by randomly initiating the centroid (the value of the considered dimensions) of each cluster. From now, the process, aiming at creating homogenous clusters, is iterative until a final solution is found. For each case, the distance from the centroid of each cluster is computed, and cases are assigned to the closest cluster. After this step, k-means computes the new values of the centroid of each cluster, as the means of all the cases belonging to the cluster. The process stops when the distance between the cases and the centroid is not decreasing anymore. It is noteworthy that the final result...
