Module « scipy.cluster.hierarchy »
Signature de la fonction median
def median(y)
Description
median.__doc__
Perform median/WPGMC linkage.
See `linkage` for more information on the return structure
and algorithm.
The following are common calling conventions:
1. ``Z = median(y)``
Performs median/WPGMC linkage on the condensed distance matrix
``y``. See ``linkage`` for more information on the return
structure and algorithm.
2. ``Z = median(X)``
Performs median/WPGMC linkage on the observation matrix ``X``
using Euclidean distance as the distance metric. See `linkage`
for more information on the return structure and algorithm.
Parameters
----------
y : ndarray
A condensed distance matrix. A condensed
distance matrix is a flat array containing the upper
triangular of the distance matrix. This is the form that
``pdist`` returns. Alternatively, a collection of
m observation vectors in n dimensions may be passed as
an m by n array.
Returns
-------
Z : ndarray
The hierarchical clustering encoded as a linkage matrix.
See Also
--------
linkage : for advanced creation of hierarchical clusterings.
scipy.spatial.distance.pdist : pairwise distance metrics
Examples
--------
>>> from scipy.cluster.hierarchy import median, 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 = median(y)
>>> Z
array([[ 0. , 1. , 1. , 2. ],
[ 3. , 4. , 1. , 2. ],
[ 9. , 10. , 1. , 2. ],
[ 6. , 7. , 1. , 2. ],
[ 2. , 12. , 1.11803399, 3. ],
[ 5. , 13. , 1.11803399, 3. ],
[ 8. , 15. , 1.11803399, 3. ],
[11. , 14. , 1.11803399, 3. ],
[18. , 19. , 3. , 6. ],
[16. , 17. , 3.5 , 6. ],
[20. , 21. , 3.25 , 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, 1, 2, 3, 4, 5, 6], dtype=int32)
>>> fcluster(Z, 1.1, criterion='distance')
array([5, 5, 6, 7, 7, 8, 1, 1, 2, 3, 3, 4], dtype=int32)
>>> fcluster(Z, 2, criterion='distance')
array([3, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2], dtype=int32)
>>> fcluster(Z, 4, 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.
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