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ParametersReturns
average(y)

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.

Perform average/UPGMA linkage on a condensed distance matrix.

See Also

linkage

for advanced creation of hierarchical clusterings.

scipy.spatial.distance.pdist

pairwise distance metrics

Examples

from scipy.cluster.hierarchy import average, 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 = average(y)
Z
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')
Also, `scipy.cluster.hierarchy.dendrogram` can be used to generate a plot of the dendrogram.
See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

scipy.spatial.distance.pdistpdistlinkagelinkage

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

GitHub : /scipy/cluster/hierarchy.py#367
type: <class 'function'>
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