is_monotonic#
- scipy.cluster.hierarchy.is_monotonic(Z)[source]#
- Return True if the linkage passed is monotonic. - The linkage is monotonic if for every cluster \(s\) and \(t\) joined, the distance between them is no less than the distance between any previously joined clusters. - Parameters:
- Zndarray
- The linkage matrix to check for monotonicity. 
 
- Returns:
- bbool
- A boolean indicating whether the linkage is monotonic. 
 
 - See also - linkage
- for a description of what a linkage matrix is. 
 - Examples - >>> from scipy.cluster.hierarchy import median, ward, is_monotonic >>> from scipy.spatial.distance import pdist - By definition, some hierarchical clustering algorithms - such as - scipy.cluster.hierarchy.ward- produce monotonic assignments of samples to clusters; however, this is not always true for other hierarchical methods - e.g.- scipy.cluster.hierarchy.median.- Given a linkage matrix - Z(as the result of a hierarchical clustering method) we can test programmatically whether it has the monotonicity property or not, using- scipy.cluster.hierarchy.is_monotonic:- >>> 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]] - >>> Z = ward(pdist(X)) >>> 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. ]]) >>> is_monotonic(Z) True - >>> Z = median(pdist(X)) >>> 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. ]]) >>> is_monotonic(Z) False - Note that this method is equivalent to just verifying that the distances in the third column of the linkage matrix appear in a monotonically increasing order.