`scipy.cluster.hierarchy._hierarchy_impl:is_isomorphic`

source: /scipy/cluster/hierarchy/_hierarchy_impl.py:3707

Signature

def is_isomorphic(T1, T2)

Summary

Determine if two different cluster assignments are equivalent.

Parameters

T1 : array_like: An assignment of singleton cluster ids to flat cluster ids.
T2 : array_like: An assignment of singleton cluster ids to flat cluster ids.

Returns

b : bool: Whether the flat cluster assignments T1 and T2 are equivalent.

Notes

Array API Standard Support

is_isomorphic 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                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

from scipy.cluster.hierarchy import fcluster, is_isomorphic
from scipy.cluster.hierarchy import single, complete
from scipy.spatial.distance import pdist

✓

Two flat cluster assignments can be isomorphic if they represent the same cluster assignment, with different labels. For example, we can use the `scipy.cluster.hierarchy.single` method and flatten the output to four clusters:

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 = single(pdist(X))
T = fcluster(Z, 1, criterion='distance')
T

✓

array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)

We can then do the same using the `scipy.cluster.hierarchy.complete`: method:

Z = complete(pdist(X))
T_ = fcluster(Z, 1.5, criterion='distance')
T_

✓

array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)

As we can see, in both cases we obtain four clusters and all the data points are distributed in the same way - the only thing that changes are the flat cluster labels (3 => 1, 4 =>2, 2 =>3 and 4 =>1), so both cluster assignments are isomorphic:

is_isomorphic(T, T_)

✗

np.True_

`scipy.cluster.hierarchy._hierarchy_impl:is_isomorphic`

Signature

Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package