Posterior probability convergence of k-NN classification and K-means clustering

Centroid based clustering methods, such as K-Means, form Voronoi cells whose radii are inversely proportional to number of clusters, K, and the expectation of posterior probability distribution in the closest cluster is related to that of a k-Nearest Neighbor Classifier (k-NN) due to the Law of Large Numbers. The aim of this study is to examine the relationship of these two seemingly different concepts of clustering and classification, more specifically, the relationship between k of k-NN and K of K-Means. One specific application area of this correspondence is local learning. The study provides experimental convergence evidence and complexity analysis to address the relative advantages of two methods in local learning applications.