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Module « scipy.cluster.hierarchy »

Fonction average - module scipy.cluster.hierarchy

Signature de la fonction average

def average(y) 

Description

help(scipy.cluster.hierarchy.average)

Perform average/UPGMA linkage on a condensed distance matrix.

Parameters
----------
y : ndarray
    The upper triangular of the distance matrix. The result of
    ``pdist`` is returned in this form.

Returns
-------
Z : ndarray
    A linkage matrix containing the hierarchical clustering. See
    `linkage` for more information on its structure.

See Also
--------
linkage : for advanced creation of hierarchical clusterings.
scipy.spatial.distance.pdist : pairwise distance metrics

Examples
--------
>>> from scipy.cluster.hierarchy import average, 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 = average(y)
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
       [ 3.        ,  4.        ,  1.        ,  2.        ],
       [ 6.        ,  7.        ,  1.        ,  2.        ],
       [ 9.        , 10.        ,  1.        ,  2.        ],
       [ 2.        , 12.        ,  1.20710678,  3.        ],
       [ 5.        , 13.        ,  1.20710678,  3.        ],
       [ 8.        , 14.        ,  1.20710678,  3.        ],
       [11.        , 15.        ,  1.20710678,  3.        ],
       [16.        , 17.        ,  3.39675184,  6.        ],
       [18.        , 19.        ,  3.39675184,  6.        ],
       [20.        , 21.        ,  4.09206523, 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([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
>>> fcluster(Z, 1.5, criterion='distance')
array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
>>> fcluster(Z, 4, criterion='distance')
array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], dtype=int32)
>>> fcluster(Z, 6, 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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