`scipy.cluster.hierarchy._hierarchy_impl:maxRstat`

source: /scipy/cluster/hierarchy/_hierarchy_impl.py:3987

Signature

def maxRstat(Z, R, i)

Summary

Return the maximum statistic for each non-singleton cluster and its children.

Parameters

Z : array_like: The hierarchical clustering encoded as a matrix. See linkage for more information.
R : array_like: The inconsistency matrix.
i : int: The column of R to use as the statistic.

Returns

MR : ndarray: Calculates the maximum statistic for the i'th column of the inconsistency matrix R for each non-singleton cluster node. MR[j] is the maximum over R[Q(j)-n, i], where Q(j) the set of all node ids corresponding to nodes below and including j.

Notes

Array API Standard Support

maxRstat 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, inconsistent, maxRstat
from scipy.spatial.distance import pdist

✓

Given a data set ``X``, we can apply a clustering method to obtain a linkage matrix ``Z``. `scipy.cluster.hierarchy.inconsistent` can be also used to obtain the inconsistency matrix ``R`` associated to this clustering process:

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))
R = inconsistent(Z)

✓

✗

array([[1.     , 0.     , 1.     , 0.     ],
       [1.     , 0.     , 1.     , 0.     ],
       [1.     , 0.     , 1.     , 0.     ],
       [1.     , 0.     , 1.     , 0.     ],
       [1.05902, 0.08346, 2.     , 0.70711],
       [1.05902, 0.08346, 2.     , 0.70711],
       [1.05902, 0.08346, 2.     , 0.70711],
       [1.05902, 0.08346, 2.     , 0.70711],
       [1.74536, 1.08655, 3.     , 1.1547 ],
       [1.91202, 1.37523, 3.     , 1.1547 ],
       [3.25   , 0.25   , 3.     , 0.     ]])

`scipy.cluster.hierarchy.maxRstat` can be used to compute the maximum value of each column of ``R``, for each non-singleton cluster and its children:

maxRstat(Z, R, 0)
maxRstat(Z, R, 1)
maxRstat(Z, R, 3)

✗

array([0.     , 0.     , 0.     , 0.     , 0.70711, 0.70711, 0.70711,
       0.70711, 1.1547 , 1.1547 , 1.1547 ])

Aliases

scipy.cluster.hierarchy.maxRstat