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Module « scipy.cluster.hierarchy »

Fonction ward - module scipy.cluster.hierarchy

Signature de la fonction ward

def ward(y) 

Description

help(scipy.cluster.hierarchy.ward)

Perform Ward's linkage on a condensed distance matrix.

See `linkage` for more information on the return structure
and algorithm.

The following are common calling conventions:

1. ``Z = ward(y)``
   Performs Ward's linkage on the condensed distance matrix ``y``.

2. ``Z = ward(X)``
   Performs Ward's linkage on the observation matrix ``X`` using
   Euclidean distance as the distance metric.

Parameters
----------
y : ndarray
    A condensed distance matrix. A condensed
    distance matrix is a flat array containing the upper
    triangular of the distance matrix. This is the form that
    ``pdist`` returns.  Alternatively, a collection of
    m observation vectors in n dimensions may be passed as
    an m by n array.

Returns
-------
Z : ndarray
    The hierarchical clustering encoded as a linkage matrix. See
    `linkage` for more information on the return structure and
    algorithm.

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

Examples
--------
>>> from scipy.cluster.hierarchy import ward, 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 = ward(y)
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
       [ 3.        ,  4.        ,  1.        ,  2.        ],
       [ 6.        ,  7.        ,  1.        ,  2.        ],
       [ 9.        , 10.        ,  1.        ,  2.        ],
       [ 2.        , 12.        ,  1.29099445,  3.        ],
       [ 5.        , 13.        ,  1.29099445,  3.        ],
       [ 8.        , 14.        ,  1.29099445,  3.        ],
       [11.        , 15.        ,  1.29099445,  3.        ],
       [16.        , 17.        ,  5.77350269,  6.        ],
       [18.        , 19.        ,  5.77350269,  6.        ],
       [20.        , 21.        ,  8.16496581, 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, 1.1, criterion='distance')
array([1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8], dtype=int32)
>>> fcluster(Z, 3, criterion='distance')
array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
>>> fcluster(Z, 9, 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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