`scipy.cluster.hierarchy._hierarchy_impl:complete`

source: /scipy/cluster/hierarchy/_hierarchy_impl.py:167

Signature

def complete(y)

Summary

Perform complete/max/farthest point 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 the linkage function documentation for more information on its structure.

Notes

Array API Standard Support

complete 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 complete, 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 = complete(y)

✓

✗

array([[ 0.     ,  1.     ,  1.     ,  2.     ],
       [ 3.     ,  4.     ,  1.     ,  2.     ],
       [ 6.     ,  7.     ,  1.     ,  2.     ],
       [ 9.     , 10.     ,  1.     ,  2.     ],
       [ 2.     , 12.     ,  1.41421,  3.     ],
       [ 5.     , 13.     ,  1.41421,  3.     ],
       [ 8.     , 14.     ,  1.41421,  3.     ],
       [11.     , 15.     ,  1.41421,  3.     ],
       [16.     , 17.     ,  4.12311,  6.     ],
       [18.     , 19.     ,  4.12311,  6.     ],
       [20.     , 21.     ,  5.65685, 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, 4.5, 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.complete