`scipy.cluster.hierarchy:ward`

source: /scipy/cluster/hierarchy.py :713

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.

Notes

Array API Standard Support

ward 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                  ⚠️ merges chunks      n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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)

✓

✗

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')

✓

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

Aliases

scipy.cluster.hierarchy.ward