# 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

`linkage`

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.