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Module « scipy.cluster.hierarchy »

Fonction single - module scipy.cluster.hierarchy

Signature de la fonction single

def single(y) 

Description

help(scipy.cluster.hierarchy.single)

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.

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