scipy.cluster.hierarchy.

maxRstat#

scipy.cluster.hierarchy.maxRstat(Z, R, i)[source]#

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

Parameters:
Zarray_like

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

Rarray_like

The inconsistency matrix.

iint

The column of R to use as the statistic.

Returns:
MRndarray

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.

See also

linkage

for a description of what a linkage matrix is.

inconsistent

for the creation of a inconsistency matrix.

Notes

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 Support for the array API standard 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)
>>> R
array([[1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.        , 0.        , 1.        , 0.        ],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.05901699, 0.08346263, 2.        , 0.70710678],
       [1.74535599, 1.08655358, 3.        , 1.15470054],
       [1.91202266, 1.37522872, 3.        , 1.15470054],
       [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)
array([1.        , 1.        , 1.        , 1.        , 1.05901699,
       1.05901699, 1.05901699, 1.05901699, 1.74535599, 1.91202266,
       3.25      ])
>>> maxRstat(Z, R, 1)
array([0.        , 0.        , 0.        , 0.        , 0.08346263,
       0.08346263, 0.08346263, 0.08346263, 1.08655358, 1.37522872,
       1.37522872])
>>> maxRstat(Z, R, 3)
array([0.        , 0.        , 0.        , 0.        , 0.70710678,
       0.70710678, 0.70710678, 0.70710678, 1.15470054, 1.15470054,
       1.15470054])
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