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Module « scipy.cluster.hierarchy »

Fonction is_monotonic - module scipy.cluster.hierarchy

Signature de la fonction is_monotonic

def is_monotonic(Z) 

Description

help(scipy.cluster.hierarchy.is_monotonic)

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.

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