Module « scipy.cluster.hierarchy »

Fonction is_valid_linkage - module scipy.cluster.hierarchy

Signature de la fonction is_valid_linkage

def is_valid_linkage(Z, warning=False, throw=False, name=None) 

Description

is_valid_linkage.__doc__

    Check the validity of a linkage matrix.

    A linkage matrix is valid if it is a 2-D array (type double)
    with :math:`n` rows and 4 columns. The first two columns must contain
    indices between 0 and :math:`2n-1`. For a given row ``i``, the following
    two expressions have to hold:

    .. math::

        0 \leq \mathtt{Z[i,0]} \leq i+n-1
        0 \leq Z[i,1] \leq i+n-1

    I.e., a cluster cannot join another cluster unless the cluster being joined
    has been generated.

    Parameters
    ----------
    Z : array_like
        Linkage matrix.
    warning : bool, optional
        When True, issues a Python warning if the linkage
        matrix passed is invalid.
    throw : bool, optional
        When True, throws a Python exception if the linkage
        matrix passed is invalid.
    name : str, optional
        This string refers to the variable name of the invalid
        linkage matrix.

    Returns
    -------
    b : bool
        True if the inconsistency matrix is valid.

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

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

    All linkage matrices generated by the clustering methods in this module
    will be valid (i.e., they will have the appropriate dimensions and the two
    required expressions will hold for all the rows).

    We can check this using `scipy.cluster.hierarchy.is_valid_linkage`:

    >>> 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_valid_linkage(Z)
    True

    However, if we create a linkage matrix in a wrong way - or if we modify
    a valid one in a way that any of the required expressions don't hold
    anymore, then the check will fail:

    >>> Z[3][1] = 20    # the cluster number 20 is not defined at this point
    >>> is_valid_linkage(Z)
    False