scipy.cluster.hierarchy.

maxinconsts#

scipy.cluster.hierarchy.maxinconsts(Z, R)[source]#

Return the maximum inconsistency coefficient for each non-singleton cluster and its children.

Parameters:
Zndarray

The hierarchical clustering encoded as a matrix. See linkage for more information.

Rndarray

The inconsistency matrix.

Returns:
MIndarray

A monotonic (n-1)-sized numpy array of doubles.

See also

linkage

for a description of what a linkage matrix is.

inconsistent

for the creation of a inconsistency matrix.

Notes

Array API Standard Support

maxinconsts has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

✅

n/a

CuPy

n/a

⛔

PyTorch

✅

⛔

JAX

✅

⛔

Dask

⚠️ merges chunks

n/a

See Support for the array API standard for more information.

Examples

>>> from scipy.cluster.hierarchy import median, inconsistent, maxinconsts
>>> 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 = median(pdist(X))
>>> R = inconsistent(Z)
>>> 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.        ]])
>>> R
array([[1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.74535599, 1.08655358, 3.        , 1.15470054],
       [1.91202266, 1.37522872, 3.        , 1.15470054],
       [3.25      , 0.25      , 3.        , 0.        ]])

Here, scipy.cluster.hierarchy.maxinconsts can be used to compute the maximum value of the inconsistency statistic (the last column of R) for each non-singleton cluster and its children:

>>> maxinconsts(Z, R)
array([0.        , 0.        , 0.        , 0.        , 0.70710678,
       0.70710678, 0.70710678, 0.70710678, 1.15470054, 1.15470054,
       1.15470054])
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