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

Rndarray

The inconsistency matrix to check for validity.

warningbool, optional

When True, issues a Python warning if the linkage matrix passed is invalid.

throwbool, optional

When True, throws a Python exception if the linkage matrix passed is invalid.

namestr, optional

This string refers to the variable name of the invalid linkage matrix.

Returns

bbool

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