`scipy.cluster.hierarchy:is_valid_linkage`

source: /scipy/cluster/hierarchy.py :2220

Signature

   def     is_valid_linkage (    Z    ,    warning    =  False   ,    throw    =  False   ,    name    =  None     )

Summary

Check the validity of a linkage matrix.

Extended Summary

A linkage matrix is valid if it is a 2-D array (type double) with $n$ rows and 4 columns. The first two columns must contain indices between 0 and $2 n - 1$ . For a given row i, the following two expressions have to hold:

0 \leq Z [i, 0] \leq i + n - 10 \leq Z [i, 1] \leq i + n - 1

I.e., a cluster cannot join another cluster unless the cluster being joined has been generated.

The fourth column of Z represents the number of original observations in a cluster, so a valid Z[i, 3] value may not exceed the number of original observations.

Parameters

Z : array_like: Linkage matrix.
warning : bool, optional: When True, issues a Python warning if the linkage matrix passed is invalid.
throw : bool, optional: When True, throws a Python exception if the linkage matrix passed is invalid.
name : str, optional: This string refers to the variable name of the invalid linkage matrix.

Returns

b : bool: True if the inconsistency matrix is valid; False otherwise.

Notes

Array API support (experimental): If the input is a lazy Array (e.g. Dask or JAX), the return value may be a 0-dimensional bool Array. When warning=True or throw=True, calling this function materializes the array.

Array API Standard Support

is_valid_linkage 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                   ⚠️ see notes          ⚠️ see notes        
Dask                  ⚠️ see notes          n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

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

✓

All linkage matrices generated by the clustering methods in this module will be valid (i.e., they will have the appropriate dimensions and the two required expressions will hold for all the rows). We can check this using `scipy.cluster.hierarchy.is_valid_linkage`:

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))

✓

✗

is_valid_linkage(Z)

✓

However, if we create a linkage matrix in a wrong way - or if we modify a valid one in a way that any of the required expressions don't hold anymore, then the check will fail:

Z[3][1] = 20    # the cluster number 20 is not defined at this point
is_valid_linkage(Z)

✓

Aliases

scipy.cluster.hierarchy.is_valid_linkage