`scipy.cluster.hierarchy._hierarchy_impl:average`

source: build-install/usr/lib/python3.14/site-packages/scipy/cluster/hierarchy/_hierarchy_impl.py:251

Signature

def average(y)

Summary

Perform average/UPGMA linkage on a condensed distance matrix.

Parameters

y : ndarray: The upper triangular of the distance matrix. The result of pdist is returned in this form.

Returns

Z : ndarray: A linkage matrix containing the hierarchical clustering. See linkage for more information on its structure.

Examples

from scipy.cluster.hierarchy import average, fcluster
from scipy.spatial.distance import pdist

✓

First, we need a toy dataset to play with:: x x x x x x x x x x x 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]]

✓

Then, we get a condensed distance matrix from this dataset:

y = pdist(X)

✓

Finally, we can perform the clustering:

Z = average(y)

✓

✗

array([[ 0.     ,  1.     ,  1.     ,  2.     ],
       [ 3.     ,  4.     ,  1.     ,  2.     ],
       [ 6.     ,  7.     ,  1.     ,  2.     ],
       [ 9.     , 10.     ,  1.     ,  2.     ],
       [ 2.     , 12.     ,  1.20711,  3.     ],
       [ 5.     , 13.     ,  1.20711,  3.     ],
       [ 8.     , 14.     ,  1.20711,  3.     ],
       [11.     , 15.     ,  1.20711,  3.     ],
       [16.     , 17.     ,  3.39675,  6.     ],
       [18.     , 19.     ,  3.39675,  6.     ],
       [20.     , 21.     ,  4.09207, 12.     ]])

The linkage matrix ``Z`` represents a dendrogram - see `scipy.cluster.hierarchy.linkage` for a detailed explanation of its contents. We can use `scipy.cluster.hierarchy.fcluster` to see to which cluster each initial point would belong given a distance threshold:

fcluster(Z, 0.9, criterion='distance')
fcluster(Z, 1.5, criterion='distance')
fcluster(Z, 4, criterion='distance')
fcluster(Z, 6, criterion='distance')

✓

array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)

Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a plot of the dendrogram.

Aliases