k-means clustering - Wikipedia, the free encyclopedia



k-means clustering - Wikipedia, the free encyclopedia

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. Contents 1 , x 2 , …, x n ), where each observation is a d-dimensional real vector, k-means clustering aims to partition the n observations into k (≤ n) sets S = {S 1 , S 2 , …, S k } so as to minimize the within-cluster sum of squares (WCSS). In other words, its objective is to find: where μ i The term "k-means" was first used by James MacQueen in 1967, [1] though the idea goes back to Hugo Steinhaus in 1957.

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