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# scipy.cluster.hierarchy.single

scipy.cluster.hierarchy.single(y)

  Perform single/min/nearest linkage on the condensed distance matrix `y`.

  Parameters:
    y ndarray

      The upper triangular of the distance matrix. The result of `pdist` is returned in this form.

  Returns:
    Z ndarray

      The linkage matrix.

  See also

  `linkage`

    for advanced creation of hierarchical clusterings.

  `scipy.spatial.distance.pdist`

    pairwise distance metrics

  Examples

      >>> from scipy.cluster.hierarchy import single, fcluster
      >>> from scipy.spatial.distance import pdist

  First, we need a toy dataset to play with:

      x x    x x
      x        x

      x        x
      x x    x x

      >>> X = [[0, 0], [0, 1], [1, 0],
      ...      [0, 4], [0, 3], [1, 4],
      ...      [4, 0], [3, 0], [4, 1],
      ...      [4, 4], [3, 4], [4, 3]]

  Then, we get a condensed distance matrix from this dataset:

      >>> y = pdist(X)

  Finally, we can perform the clustering:

      >>> Z = single(y)
      >>> Z
      array([[ 0.,  1.,  1.,  2.],
             [ 2., 12.,  1.,  3.],
             [ 3.,  4.,  1.,  2.],
             [ 5., 14.,  1.,  3.],
             [ 6.,  7.,  1.,  2.],
             [ 8., 16.,  1.,  3.],
             [ 9., 10.,  1.,  2.],
             [11., 18.,  1.,  3.],
             [13., 15.,  2.,  6.],
             [17., 20.,  2.,  9.],
             [19., 21.,  2., 12.]])

  The linkage matrix `Z` represents a dendrogram - see `scipy.cluster.hierarchy.linkage` for a detailed explanation of its contents.

  We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster each initial point would belong given a distance threshold:

      >>> fcluster(Z, 0.9, criterion='distance')
      array([ 7,  8,  9, 10, 11, 12,  4,  5,  6,  1,  2,  3], dtype=int32)
      >>> fcluster(Z, 1, criterion='distance')
      array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)
      >>> fcluster(Z, 2, criterion='distance')
      array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)

  Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a plot of the dendrogram.