scipy.cluster.hierarchy.complete#
- scipy.cluster.hierarchy.complete(y)[source]#
Perform complete/max/farthest point linkage on a condensed distance matrix.
- Parameters:
- yndarray
The upper triangular of the distance matrix. The result of
pdist
is returned in this form.
- Returns:
- Zndarray
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 - seescipy.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.