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.

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 algorithms. 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.

The algorithm has nothing to do with and should not be confused with k-nearest neighbor another popular machine learning technique.