Module « scipy.cluster.hierarchy »

Fonction is_monotonic - module scipy.cluster.hierarchy

Signature de la fonction is_monotonic

def is_monotonic(Z) 

Description

is_monotonic.__doc__

    Return True if the linkage passed is monotonic.

    The linkage is monotonic if for every cluster :math:`s` and :math:`t`
    joined, the distance between them is no less than the distance
    between any previously joined clusters.

    Parameters
    ----------
    Z : ndarray
        The linkage matrix to check for monotonicity.

    Returns
    -------
    b : bool
        A boolean indicating whether the linkage is monotonic.

    See Also
    --------
    linkage : for a description of what a linkage matrix is.

    Examples
    --------
    >>> from scipy.cluster.hierarchy import median, ward, is_monotonic
    >>> from scipy.spatial.distance import pdist

    By definition, some hierarchical clustering algorithms - such as
    `scipy.cluster.hierarchy.ward` - produce monotonic assignments of
    samples to clusters; however, this is not always true for other
    hierarchical methods - e.g. `scipy.cluster.hierarchy.median`.

    Given a linkage matrix ``Z`` (as the result of a hierarchical clustering
    method) we can test programmatically whether it has the monotonicity
    property or not, using `scipy.cluster.hierarchy.is_monotonic`:

    >>> 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]]

    >>> Z = ward(pdist(X))
    >>> 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.        ]])
    >>> is_monotonic(Z)
    True

    >>> Z = median(pdist(X))
    >>> Z
    array([[ 0.        ,  1.        ,  1.        ,  2.        ],
           [ 3.        ,  4.        ,  1.        ,  2.        ],
           [ 9.        , 10.        ,  1.        ,  2.        ],
           [ 6.        ,  7.        ,  1.        ,  2.        ],
           [ 2.        , 12.        ,  1.11803399,  3.        ],
           [ 5.        , 13.        ,  1.11803399,  3.        ],
           [ 8.        , 15.        ,  1.11803399,  3.        ],
           [11.        , 14.        ,  1.11803399,  3.        ],
           [18.        , 19.        ,  3.        ,  6.        ],
           [16.        , 17.        ,  3.5       ,  6.        ],
           [20.        , 21.        ,  3.25      , 12.        ]])
    >>> is_monotonic(Z)
    False

    Note that this method is equivalent to just verifying that the distances
    in the third column of the linkage matrix appear in a monotonically
    increasing order.