scipy.cluster.hierarchy.is_isomorphic#
- scipy.cluster.hierarchy.is_isomorphic(T1, T2)[source]#
Determine if two different cluster assignments are equivalent.
- Parameters:
- T1array_like
An assignment of singleton cluster ids to flat cluster ids.
- T2array_like
An assignment of singleton cluster ids to flat cluster ids.
- Returns:
- bbool
Whether the flat cluster assignments T1 and T2 are equivalent.
See also
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_) True