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

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

>>> fromscipy.cluster.hierarchyimport median, inconsistent, maxinconsts
>>> fromscipy.spatial.distanceimport 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])