KMeans

KMeans[data, seeds] returns a clustering of data by minimizing the within-cluster sums-of-squares, given initial estimates for the cluster centers, seeds.

KMeans[data, seeds, weights] returns a clustering of data by minimizing the within-cluster sums-of-squares, given initial estimates for the cluster centers, seeds, and weights for each element of the measurement vectors in data.

The argument data is a list of n-element measurement vectors, seeds is a list of n-element vectors denoting the initial estimates of the cluster centers, and weights, if given, is an n-element vector. The length of the argument seeds determines the number of clusters returned by KMeans.

The default option DistanceFunction → EuclideanDistance selects the Euclidean distance metric for use in KMeans. Other common distance functions include ManhattanDistance, ChebyshevDistance, CanberraDistance, and MinkowskiDistance.

The option MaxRecursion → 15 limits the maximum number of iterations of the algorithm.

See also User's Guide 7.5 and the tutorial Partitioning Data into Clusters.

Modified in Version 2.2.

Example

This loads the package.

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This defines three seeds.

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This generates the example data.

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Here is a scatter plot of the data.

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This finds a grouping of the data that minimizes the within-cluster Euclidean distance.

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This plots the result using different colors for each of the clusters.

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This computes two alternative groupings of the data.

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This shows the two results.

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