scipy.cluster.hierarchy.complete

scipy.cluster.hierarchy.complete(y)

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.

See also

linkage

for advanced creation of hierarchical clusterings.

scipy.spatial.distance.pdist

pairwise distance metrics

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)
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
       [ 3.        ,  4.        ,  1.        ,  2.        ],
       [ 6.        ,  7.        ,  1.        ,  2.        ],
       [ 9.        , 10.        ,  1.        ,  2.        ],
       [ 2.        , 12.        ,  1.41421356,  3.        ],
       [ 5.        , 13.        ,  1.41421356,  3.        ],
       [ 8.        , 14.        ,  1.41421356,  3.        ],
       [11.        , 15.        ,  1.41421356,  3.        ],
       [16.        , 17.        ,  4.12310563,  6.        ],
       [18.        , 19.        ,  4.12310563,  6.        ],
       [20.        , 21.        ,  5.65685425, 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')
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12], dtype=int32)
>>> fcluster(Z, 1.5, criterion='distance')
array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)
>>> fcluster(Z, 4.5, criterion='distance')
array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], dtype=int32)
>>> 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.