scipy.cluster.hierarchy.ward#
- scipy.cluster.hierarchy.ward(y)[source]#
Perform Ward’s linkage on a condensed distance matrix.
See
linkage
for more information on the return structure and algorithm.The following are common calling conventions:
Z = ward(y)
Performs Ward’s linkage on the condensed distance matrixy
.Z = ward(X)
Performs Ward’s linkage on the observation matrixX
using Euclidean distance as the distance metric.
- Parameters:
- yndarray
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:
- Zndarray
The hierarchical clustering encoded as a linkage matrix. See
linkage
for more information on the return structure and algorithm.
See also
linkage
for advanced creation of hierarchical clusterings.
scipy.spatial.distance.pdist
pairwise distance metrics
Examples
>>> from scipy.cluster.hierarchy import ward, 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 = ward(y) >>> Z array([[ 0. , 1. , 1. , 2. ], [ 3. , 4. , 1. , 2. ], [ 6. , 7. , 1. , 2. ], [ 9. , 10. , 1. , 2. ], [ 2. , 12. , 1.29099445, 3. ], [ 5. , 13. , 1.29099445, 3. ], [ 8. , 14. , 1.29099445, 3. ], [11. , 15. , 1.29099445, 3. ], [16. , 17. , 5.77350269, 6. ], [18. , 19. , 5.77350269, 6. ], [20. , 21. , 8.16496581, 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, 1.1, criterion='distance') array([1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8], dtype=int32) >>> fcluster(Z, 3, criterion='distance') array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32) >>> fcluster(Z, 9, 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.