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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

help(scipy.cluster.hierarchy.is_valid_linkage)

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

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