<Tr> <Td> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> k - means clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining . k - means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster . This results in a partitioning of the data space into Voronoi cells . </P> <P> The problem is computationally difficult (NP - hard); however, there are efficient heuristic algorithms that are commonly employed and converge quickly to a local optimum . These are usually similar to the expectation - maximization algorithm for mixtures of Gaussian distributions via an iterative refinement approach employed by both k - means and Gaussian mixture modeling . Additionally, they both use cluster centers to model the data; however, k - means clustering tends to find clusters of comparable spatial extent, while the expectation - maximization mechanism allows clusters to have different shapes . </P>

What is frequently referred to as k - means clustering