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bundles / scipy 2.0.0.dev0+git20260907.41eeb59 / scipy / cluster / hierarchy / _hierarchy_impl / cophenet

function

scipy.cluster.hierarchy._hierarchy_impl:cophenet

source: build-install/usr/lib/python3.14/site-packages/scipy/cluster/hierarchy/_hierarchy_impl.py:1485

Signature

def cophenet(Z, Y = None)

Summary

Calculate the cophenetic distances between each observation in the hierarchical clustering defined by the linkage Z.

Extended Summary

Suppose p and q are original observations in disjoint clusters s and t, respectively and s and t are joined by a direct parent cluster u. The cophenetic distance between observations i and j is simply the distance between clusters s and t.

Parameters

Z : ndarray

The hierarchical clustering encoded as an array (see linkage function).

Y : ndarray (optional)

Calculates the cophenetic correlation coefficient c of a hierarchical clustering defined by the linkage matrix Z of a set of observations in dimensions. Y is the condensed distance matrix from which Z was generated.

Returns

c : ndarray

The cophentic correlation distance (if Y is passed).

d : ndarray

The cophenetic distance matrix in condensed form. The th entry is the cophenetic distance between original observations and .

Examples

from scipy.cluster.hierarchy import single, cophenet
from scipy.spatial.distance import pdist, squareform
✓
Given a dataset ``X`` and a linkage matrix ``Z``, the cophenetic distance between two points of ``X`` is the distance between the largest two distinct clusters that each of the points: 
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`` corresponds to this dataset :: x x x x x x x x x x x x 
Z = single(pdist(X))
Z
cophenet(Z)
✓
array([1., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 2., 2., 2., 2., 2.,
       2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 1., 2., 2.,
       2., 2., 2., 2., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2.,
       1., 1., 2., 2., 2., 1., 2., 2., 2., 2., 2., 2., 1., 1., 1.])
The output of the `scipy.cluster.hierarchy.cophenet` method is represented in condensed form. We can use `scipy.spatial.distance.squareform` to see the output as a regular matrix (where each element ``ij`` denotes the cophenetic distance between each ``i``, ``j`` pair of points in ``X``): 
squareform(cophenet(Z))
✓
array([[0., 1., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [1., 0., 1., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [1., 1., 0., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 0., 1., 1., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 1., 0., 1., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 1., 1., 0., 2., 2., 2., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 0., 1., 1., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 1., 0., 1., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 1., 1., 0., 2., 2., 2.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2., 0., 1., 1.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 0., 1.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2., 1., 1., 0.]])
In this example, the cophenetic distance between points on ``X`` that are very close (i.e., in the same corner) is 1. For other pairs of points is 2, because the points will be located in clusters at different corners - thus, the distance between these clusters will be larger.

See also

linkage

for a description of what a linkage matrix is.

scipy.spatial.distance.squareform

transforming condensed matrices into square ones.

Aliases

  • scipy.cluster.hierarchy.cophenet