`scipy.cluster.hierarchy._hierarchy_impl:weighted`

source: /scipy/cluster/hierarchy/_hierarchy_impl.py:333

Signature

def weighted(y)

Summary

Perform weighted/WPGMA linkage on the condensed distance matrix.

Extended Summary

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

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.

Notes

Array API Standard Support

weighted 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 weighted, 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 = weighted(y)

✓

✗

array([[ 0.     ,  1.     ,  1.     ,  2.     ],
       [ 6.     ,  7.     ,  1.     ,  2.     ],
       [ 3.     ,  4.     ,  1.     ,  2.     ],
       [ 9.     , 11.     ,  1.     ,  2.     ],
       [ 2.     , 12.     ,  1.20711,  3.     ],
       [ 8.     , 13.     ,  1.20711,  3.     ],
       [ 5.     , 14.     ,  1.20711,  3.     ],
       [10.     , 15.     ,  1.20711,  3.     ],
       [18.     , 19.     ,  3.05596,  6.     ],
       [16.     , 17.     ,  3.32379,  6.     ],
       [20.     , 21.     ,  4.06358, 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

scipy.cluster.hierarchy.weighted