# scipy.cluster.hierarchy.single¶

scipy.cluster.hierarchy.single(y)[source]

Perform single/min/nearest linkage on the condensed distance matrix y.

Parameters
yndarray

The upper triangular of the distance matrix. The result of pdist is returned in this form.

Returns
Zndarray

for advanced creation of hierarchical clusterings.

scipy.spatial.distance.pdist

pairwise distance metrics

Examples

>>> from scipy.cluster.hierarchy import single, 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 = single(y)
>>> Z
array([[ 0.,  1.,  1.,  2.],
[ 2., 12.,  1.,  3.],
[ 3.,  4.,  1.,  2.],
[ 5., 14.,  1.,  3.],
[ 6.,  7.,  1.,  2.],
[ 8., 16.,  1.,  3.],
[ 9., 10.,  1.,  2.],
[11., 18.,  1.,  3.],
[13., 15.,  2.,  6.],
[17., 20.,  2.,  9.],
[19., 21.,  2., 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([ 7,  8,  9, 10, 11, 12,  4,  5,  6,  1,  2,  3], dtype=int32)
>>> fcluster(Z, 1, criterion='distance')
array([3, 3, 3, 4, 4, 4, 2, 2, 2, 1, 1, 1], dtype=int32)
>>> fcluster(Z, 2, 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.