scipy.cluster.hierarchy.is_valid_im

scipy.cluster.hierarchy.is_valid_im(R, warning=False, throw=False, name=None)

Return True if the inconsistency matrix passed is valid.

It must be a \(n\) by 4 array of doubles. The standard deviations R[:,1] must be nonnegative. The link counts R[:,2] must be positive and no greater than \(n-1\).

Parameters:

R : ndarray

The inconsistency matrix to check for validity.

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.

inconsistent

for the creation of a inconsistency matrix.

Examples

>>> from scipy.cluster.hierarchy import ward, inconsistent, is_valid_im
>>> from scipy.spatial.distance import pdist

Given a data set X, we can apply a clustering method to obtain a linkage matrix Z. scipy.cluster.hierarchy.inconsistent can be also used to obtain the inconsistency matrix R associated to this clustering process:

>>> 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))
>>> R = inconsistent(Z)
>>> 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.        ]])
>>> R
array([[1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.14549722, 0.20576415, 2.        , 0.70710678],
       [1.14549722, 0.20576415, 2.        , 0.70710678],
       [1.14549722, 0.20576415, 2.        , 0.70710678],
       [1.14549722, 0.20576415, 2.        , 0.70710678],
       [2.78516386, 2.58797734, 3.        , 1.15470054],
       [2.78516386, 2.58797734, 3.        , 1.15470054],
       [6.57065706, 1.38071187, 3.        , 1.15470054]])

Now we can use scipy.cluster.hierarchy.is_valid_im to verify that R is correct:

>>> is_valid_im(R)
True

However, if R is wrongly constructed (e.g one of the standard deviations is set to a negative value) then the check will fail:

>>> R[-1,1] = R[-1,1] * -1
>>> is_valid_im(R)
False