In this post, we will look at using an iterative approach to searching for a better set of initial centroids for k-means clustering, and will do so by performing this process on a sample of our full dataset. What do we mean by "better?" Since k-means clustering aims to converge on an optimal set of cluster centers (centroids) and cluster membership based on distance from these centroids via successive iterations, it is intuitive that the more optimal the positioning of these initial centroids, the fewer iterations of the k-means clustering algorithms will be required for convergence. Therefore, thinking about ways to find a better set of initial centroid positions is a valid approach to optimizing the k-means clustering process. What we will do differently, specifically, is to draw a sample of data from our full dataset, and run short runs of of the k-means clustering algorithm on it (not to convergence), short runs which will include, out of necessity, the centroid initialization process.