scipy.cluster.hierarchy.centroid¶
-
scipy.cluster.hierarchy.
centroid
(y)[source]¶ Perform centroid/UPGMC linkage.
See
linkage
for more information on the input matrix, return structure, and algorithm.The following are common calling conventions:
Z = centroid(y)
Performs centroid/UPGMC linkage on the condensed distance matrix
y
.Z = centroid(X)
Performs centroid/UPGMC linkage on the observation matrix
X
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
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 centroid, 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 = centroid(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. , 3.33333333, 6. ], [16. , 17. , 3.33333333, 6. ], [20. , 21. , 3.33333333, 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([ 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.