ward — SciPy v1.15.2 Manual (original) (raw)

scipy.cluster.hierarchy.

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:

  1. Z = ward(y)Performs Ward’s linkage on the condensed distance matrix y.
  2. Z = ward(X)Performs Ward’s 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 thatpdist 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. Seelinkage for more information on the return structure and algorithm.

Examples

from scipy.cluster.hierarchy import ward, fcluster from scipy.spatial.distance import pdist

First, we need a toy dataset to play with:

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:

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.