scipy.cluster.hierarchy.

correspond#

scipy.cluster.hierarchy.correspond(Z, Y)[source]#

Check for correspondence between linkage and condensed distance matrices.

They must have the same number of original observations for the check to succeed.

This function is useful as a sanity check in algorithms that make extensive use of linkage and distance matrices that must correspond to the same set of original observations.

Parameters:

Zarray_like: The linkage matrix to check for correspondence.
Yarray_like: The condensed distance matrix to check for correspondence.

Returns:

bbool: A boolean indicating whether the linkage matrix and distance matrix could possibly correspond to one another.

See also

linkage: for a description of what a linkage matrix is.

Notes

Array API Standard Support

correspond 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 Support for the array API standard for more information.

Examples

>>> from scipy.cluster.hierarchy import ward, correspond
>>> from scipy.spatial.distance import pdist

This method can be used to check if a given linkage matrix Z has been obtained from the application of a cluster method over a dataset X:

>>> 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]]
>>> X_condensed = pdist(X)
>>> Z = ward(X_condensed)

Here, we can compare Z and X (in condensed form):

>>> correspond(Z, X_condensed)
True