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# scipy.cluster.vq.kmeans

`scipy.cluster.vq.``kmeans`(obs, k_or_guess, iter=20, thresh=1e-05)

  Performs k-means on a set of observation vectors forming k clusters.

  The k-means algorithm adjusts the centroids until sufficient progress cannot be made, i.e. the change in distortion since the last iteration is less than some threshold. This yields a code book mapping centroids to codes and vice versa.

  Distortion is defined as the sum of the squared differences between the observations and the corresponding centroid.

  Parameters : | obs : ndarray Each row of the M by N array is an observation vector. The columns are the features seen during each observation. The features must be whitened first with the `whiten` function. k_or_guess : int or ndarray The number of centroids to generate. A code is assigned to each centroid, which is also the row index of the centroid in the code_book matrix generated. The initial k centroids are chosen by randomly selecting observations from the observation matrix. Alternatively, passing a k by N array specifies the initial k centroids. iter : int, optional The number of times to run k-means, returning the codebook with the lowest distortion. This argument is ignored if initial centroids are specified with an array for the `k_or_guess` parameter. This parameter does not represent the number of iterations of the k-means algorithm. thresh : float, optional Terminates the k-means algorithm if the change in distortion since the last k-means iteration is less than or equal to thresh.
  Returns : | codebook : ndarray A k by N array of k centroids. The i’th centroid codebook[i] is represented with the code i. The centroids and codes generated represent the lowest distortion seen, not necessarily the globally minimal distortion. distortion : float The distortion between the observations passed and the centroids generated.

  See also

  `kmeans2`
    a different implementation of k-means clustering with more methods for generating initial centroids but without using a distortion change threshold as a stopping criterion.
  `whiten`
    must be called prior to passing an observation matrix to kmeans.

  Examples

      >>> from numpy import array
      >>> from scipy.cluster.vq import vq, kmeans, whiten
      >>> features  = array([[ 1.9,2.3],
      ...                    [ 1.5,2.5],
      ...                    [ 0.8,0.6],
      ...                    [ 0.4,1.8],
      ...                    [ 0.1,0.1],
      ...                    [ 0.2,1.8],
      ...                    [ 2.0,0.5],
      ...                    [ 0.3,1.5],
      ...                    [ 1.0,1.0]])
      >>> whitened = whiten(features)
      >>> book = array((whitened[0],whitened[2]))
      >>> kmeans(whitened,book)
      (array([[ 2.3110306 ,  2.86287398],
             [ 0.93218041,  1.24398691]]), 0.85684700941625547)

      >>> from numpy import random
      >>> random.seed((1000,2000))
      >>> codes = 3
      >>> kmeans(whitened,codes)
      (array([[ 2.3110306 ,  2.86287398],
             [ 1.32544402,  0.65607529],
             [ 0.40782893,  2.02786907]]), 0.5196582527686241)

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