`scipy.cluster.hierarchy._hierarchy_impl:ward`

source: build-install/usr/lib/python3.14/site-packages/scipy/cluster/hierarchy/_hierarchy_impl.py:623

Signature

def ward(y)

Summary

Perform Ward's linkage on a condensed distance matrix.

Extended Summary

See linkage for more information on the return structure and algorithm.

The following are common calling conventions:

Z = ward(y) Performs Ward's linkage on the condensed distance matrix y.
Z = ward(X) Performs Ward's linkage on the observation matrix X using Euclidean distance as the distance metric.

Parameters

y : ndarray: A condensed distance matrix. A condensed distance matrix is a flat array containing the upper triangular of the distance matrix. This is the form that pdist returns. Alternatively, a collection of m observation vectors in n dimensions may be passed as an m by n array.

Returns

Z : ndarray: The hierarchical clustering encoded as a linkage matrix. See linkage for more information on the return structure and algorithm.

Examples

from scipy.cluster.hierarchy import ward, 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 = ward(y)

✓

✗

array([[ 0.     ,  1.     ,  1.     ,  2.     ],
       [ 3.     ,  4.     ,  1.     ,  2.     ],
       [ 6.     ,  7.     ,  1.     ,  2.     ],
       [ 9.     , 10.     ,  1.     ,  2.     ],
       [ 2.     , 12.     ,  1.29099,  3.     ],
       [ 5.     , 13.     ,  1.29099,  3.     ],
       [ 8.     , 14.     ,  1.29099,  3.     ],
       [11.     , 15.     ,  1.29099,  3.     ],
       [16.     , 17.     ,  5.7735 ,  6.     ],
       [18.     , 19.     ,  5.7735 ,  6.     ],
       [20.     , 21.     ,  8.16497, 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, 1.1, criterion='distance')
fcluster(Z, 3, criterion='distance')
fcluster(Z, 9, 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

scipy.cluster.hierarchy.ward