Module « scipy.cluster.hierarchy »

Fonction ward - module scipy.cluster.hierarchy

Signature de la fonction ward

def ward(y) 

Description

ward.__doc__

    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.