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Module « scipy.cluster.hierarchy »

Fonction leaders - module scipy.cluster.hierarchy

Signature de la fonction leaders

def leaders(Z, T) 

Description

help(scipy.cluster.hierarchy.leaders)

Return the root nodes in a hierarchical clustering.

Returns the root nodes in a hierarchical clustering corresponding
to a cut defined by a flat cluster assignment vector ``T``. See
the ``fcluster`` function for more information on the format of ``T``.

For each flat cluster :math:`j` of the :math:`k` flat clusters
represented in the n-sized flat cluster assignment vector ``T``,
this function finds the lowest cluster node :math:`i` in the linkage
tree Z, such that:

  * leaf descendants belong only to flat cluster j
    (i.e., ``T[p]==j`` for all :math:`p` in :math:`S(i)`, where
    :math:`S(i)` is the set of leaf ids of descendant leaf nodes
    with cluster node :math:`i`)

  * there does not exist a leaf that is not a descendant with
    :math:`i` that also belongs to cluster :math:`j`
    (i.e., ``T[q]!=j`` for all :math:`q` not in :math:`S(i)`). If
    this condition is violated, ``T`` is not a valid cluster
    assignment vector, and an exception will be thrown.

Parameters
----------
Z : ndarray
    The hierarchical clustering encoded as a matrix. See
    `linkage` for more information.
T : ndarray
    The flat cluster assignment vector.

Returns
-------
L : ndarray
    The leader linkage node id's stored as a k-element 1-D array,
    where ``k`` is the number of flat clusters found in ``T``.

    ``L[j]=i`` is the linkage cluster node id that is the
    leader of flat cluster with id M[j]. If ``i < n``, ``i``
    corresponds to an original observation, otherwise it
    corresponds to a non-singleton cluster.
M : ndarray
    The leader linkage node id's stored as a k-element 1-D array, where
    ``k`` is the number of flat clusters found in ``T``. This allows the
    set of flat cluster ids to be any arbitrary set of ``k`` integers.

    For example: if ``L[3]=2`` and ``M[3]=8``, the flat cluster with
    id 8's leader is linkage node 2.

See Also
--------
fcluster : for the creation of flat cluster assignments.

Examples
--------
>>> from scipy.cluster.hierarchy import ward, fcluster, leaders
>>> from scipy.spatial.distance import pdist

Given a linkage matrix ``Z`` - obtained after apply a clustering method
to a dataset ``X`` - and a flat cluster assignment array ``T``:

>>> 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))
>>> Z
array([[ 0.        ,  1.        ,  1.        ,  2.        ],
       [ 3.        ,  4.        ,  1.        ,  2.        ],
       [ 6.        ,  7.        ,  1.        ,  2.        ],
       [ 9.        , 10.        ,  1.        ,  2.        ],
       [ 2.        , 12.        ,  1.29099445,  3.        ],
       [ 5.        , 13.        ,  1.29099445,  3.        ],
       [ 8.        , 14.        ,  1.29099445,  3.        ],
       [11.        , 15.        ,  1.29099445,  3.        ],
       [16.        , 17.        ,  5.77350269,  6.        ],
       [18.        , 19.        ,  5.77350269,  6.        ],
       [20.        , 21.        ,  8.16496581, 12.        ]])

>>> T = fcluster(Z, 3, criterion='distance')
>>> T
array([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], dtype=int32)

`scipy.cluster.hierarchy.leaders` returns the indices of the nodes
in the dendrogram that are the leaders of each flat cluster:

>>> L, M = leaders(Z, T)
>>> L
array([16, 17, 18, 19], dtype=int32)

(remember that indices 0-11 point to the 12 data points in ``X``,
whereas indices 12-22 point to the 11 rows of ``Z``)

`scipy.cluster.hierarchy.leaders` also returns the indices of
the flat clusters in ``T``:

>>> M
array([1, 2, 3, 4], dtype=int32)

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