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scipy.cluster.hierarchy.

# maxRstat

scipy.cluster.hierarchy.maxRstat(Z, R, i)

  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`.

  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])