`scipy.cluster.hierarchy:maxdists`

source: /scipy/cluster/hierarchy.py :3903

Signature

def maxdists ( Z )

Summary

Return the maximum distance between any non-singleton cluster.

Parameters

Z : ndarray: The hierarchical clustering encoded as a matrix. See linkage for more information.

Returns

maxdists : ndarray: A (n-1) sized numpy array of doubles; MD[i] represents the maximum distance between any cluster (including singletons) below and including the node with index i. More specifically, MD[i] = Z[Q(i)-n, 2].max() where Q(i) is the set of all node indices below and including node i.

Notes

Array API Standard Support

maxdists has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ✅                     ⛔                   
JAX                   ✅                     ⛔                   
Dask                  ⚠️ merges chunks      n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

from scipy.cluster.hierarchy import median, maxdists
from scipy.spatial.distance import pdist

✓

Given a linkage matrix ``Z``, `scipy.cluster.hierarchy.maxdists` computes for each new cluster generated (i.e., for each row of the linkage matrix) what is the maximum distance between any two child clusters. Due to the nature of hierarchical clustering, in many cases this is going to be just the distance between the two child clusters that were merged to form the current one - that is, Z[:,2]. However, for non-monotonic cluster assignments such as `scipy.cluster.hierarchy.median` clustering this is not always the case: There may be cluster formations were the distance between the two clusters merged is smaller than the distance between their children. We can see this in an example:

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 = median(pdist(X))

✓

Z
maxdists(Z)

✗

Note that while the distance between the two clusters merged when creating the last cluster is 3.25, there are two children (clusters 16 and 17) whose distance is larger (3.5). Thus, `scipy.cluster.hierarchy.maxdists` returns 3.5 in this case.

Aliases

scipy.cluster.hierarchy.maxdists