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def dendrogram(Z, p=30, truncate_mode=None, color_threshold=None, get_leaves=True, orientation='top', labels=None, count_sort=False, distance_sort=False, show_leaf_counts=True, no_plot=False, no_labels=False, leaf_font_size=None, leaf_rotation=None, leaf_label_func=None, show_contracted=False, link_color_func=None, ax=None, above_threshold_color='C0')
Plot the hierarchical clustering as a dendrogram.
The dendrogram illustrates how each cluster is
composed by drawing a U-shaped link between a non-singleton
cluster and its children. The top of the U-link indicates a
cluster merge. The two legs of the U-link indicate which clusters
were merged. The length of the two legs of the U-link represents
the distance between the child clusters. It is also the
cophenetic distance between original observations in the two
children clusters.
Parameters
----------
Z : ndarray
The linkage matrix encoding the hierarchical clustering to
render as a dendrogram. See the ``linkage`` function for more
information on the format of ``Z``.
p : int, optional
The ``p`` parameter for ``truncate_mode``.
truncate_mode : str, optional
The dendrogram can be hard to read when the original
observation matrix from which the linkage is derived is
large. Truncation is used to condense the dendrogram. There
are several modes:
``None``
No truncation is performed (default).
Note: ``'none'`` is an alias for ``None`` that's kept for
backward compatibility.
``'lastp'``
The last ``p`` non-singleton clusters formed in the linkage are the
only non-leaf nodes in the linkage; they correspond to rows
``Z[n-p-2:end]`` in ``Z``. All other non-singleton clusters are
contracted into leaf nodes.
``'level'``
No more than ``p`` levels of the dendrogram tree are displayed.
A "level" includes all nodes with ``p`` merges from the final merge.
Note: ``'mtica'`` is an alias for ``'level'`` that's kept for
backward compatibility.
color_threshold : double, optional
For brevity, let :math:`t` be the ``color_threshold``.
Colors all the descendent links below a cluster node
:math:`k` the same color if :math:`k` is the first node below
the cut threshold :math:`t`. All links connecting nodes with
distances greater than or equal to the threshold are colored
with de default matplotlib color ``'C0'``. If :math:`t` is less
than or equal to zero, all nodes are colored ``'C0'``.
If ``color_threshold`` is None or 'default',
corresponding with MATLAB(TM) behavior, the threshold is set to
``0.7*max(Z[:,2])``.
get_leaves : bool, optional
Includes a list ``R['leaves']=H`` in the result
dictionary. For each :math:`i`, ``H[i] == j``, cluster node
``j`` appears in position ``i`` in the left-to-right traversal
of the leaves, where :math:`j < 2n-1` and :math:`i < n`.
orientation : str, optional
The direction to plot the dendrogram, which can be any
of the following strings:
``'top'``
Plots the root at the top, and plot descendent links going downwards.
(default).
``'bottom'``
Plots the root at the bottom, and plot descendent links going
upwards.
``'left'``
Plots the root at the left, and plot descendent links going right.
``'right'``
Plots the root at the right, and plot descendent links going left.
labels : ndarray, optional
By default, ``labels`` is None so the index of the original observation
is used to label the leaf nodes. Otherwise, this is an :math:`n`-sized
sequence, with ``n == Z.shape[0] + 1``. The ``labels[i]`` value is the
text to put under the :math:`i` th leaf node only if it corresponds to
an original observation and not a non-singleton cluster.
count_sort : str or bool, optional
For each node n, the order (visually, from left-to-right) n's
two descendent links are plotted is determined by this
parameter, which can be any of the following values:
``False``
Nothing is done.
``'ascending'`` or ``True``
The child with the minimum number of original objects in its cluster
is plotted first.
``'descending'``
The child with the maximum number of original objects in its cluster
is plotted first.
Note, ``distance_sort`` and ``count_sort`` cannot both be True.
distance_sort : str or bool, optional
For each node n, the order (visually, from left-to-right) n's
two descendent links are plotted is determined by this
parameter, which can be any of the following values:
``False``
Nothing is done.
``'ascending'`` or ``True``
The child with the minimum distance between its direct descendents is
plotted first.
``'descending'``
The child with the maximum distance between its direct descendents is
plotted first.
Note ``distance_sort`` and ``count_sort`` cannot both be True.
show_leaf_counts : bool, optional
When True, leaf nodes representing :math:`k>1` original
observation are labeled with the number of observations they
contain in parentheses.
no_plot : bool, optional
When True, the final rendering is not performed. This is
useful if only the data structures computed for the rendering
are needed or if matplotlib is not available.
no_labels : bool, optional
When True, no labels appear next to the leaf nodes in the
rendering of the dendrogram.
leaf_rotation : double, optional
Specifies the angle (in degrees) to rotate the leaf
labels. When unspecified, the rotation is based on the number of
nodes in the dendrogram (default is 0).
leaf_font_size : int, optional
Specifies the font size (in points) of the leaf labels. When
unspecified, the size based on the number of nodes in the
dendrogram.
leaf_label_func : lambda or function, optional
When ``leaf_label_func`` is a callable function, for each
leaf with cluster index :math:`k < 2n-1`. The function
is expected to return a string with the label for the
leaf.
Indices :math:`k < n` correspond to original observations
while indices :math:`k \geq n` correspond to non-singleton
clusters.
For example, to label singletons with their node id and
non-singletons with their id, count, and inconsistency
coefficient, simply do::
# First define the leaf label function.
def llf(id):
if id < n:
return str(id)
else:
return '[%d %d %1.2f]' % (id, count, R[n-id,3])
# The text for the leaf nodes is going to be big so force
# a rotation of 90 degrees.
dendrogram(Z, leaf_label_func=llf, leaf_rotation=90)
# leaf_label_func can also be used together with ``truncate_mode``,
# in which case you will get your leaves labeled after truncation:
dendrogram(Z, leaf_label_func=llf, leaf_rotation=90,
truncate_mode='level', p=2)
show_contracted : bool, optional
When True the heights of non-singleton nodes contracted
into a leaf node are plotted as crosses along the link
connecting that leaf node. This really is only useful when
truncation is used (see ``truncate_mode`` parameter).
link_color_func : callable, optional
If given, `link_color_function` is called with each non-singleton id
corresponding to each U-shaped link it will paint. The function is
expected to return the color to paint the link, encoded as a matplotlib
color string code. For example::
dendrogram(Z, link_color_func=lambda k: colors[k])
colors the direct links below each untruncated non-singleton node
``k`` using ``colors[k]``.
ax : matplotlib Axes instance, optional
If None and `no_plot` is not True, the dendrogram will be plotted
on the current axes. Otherwise if `no_plot` is not True the
dendrogram will be plotted on the given ``Axes`` instance. This can be
useful if the dendrogram is part of a more complex figure.
above_threshold_color : str, optional
This matplotlib color string sets the color of the links above the
color_threshold. The default is ``'C0'``.
Returns
-------
R : dict
A dictionary of data structures computed to render the
dendrogram. Its has the following keys:
``'color_list'``
A list of color names. The k'th element represents the color of the
k'th link.
``'icoord'`` and ``'dcoord'``
Each of them is a list of lists. Let ``icoord = [I1, I2, ..., Ip]``
where ``Ik = [xk1, xk2, xk3, xk4]`` and ``dcoord = [D1, D2, ..., Dp]``
where ``Dk = [yk1, yk2, yk3, yk4]``, then the k'th link painted is
``(xk1, yk1)`` - ``(xk2, yk2)`` - ``(xk3, yk3)`` - ``(xk4, yk4)``.
``'ivl'``
A list of labels corresponding to the leaf nodes.
``'leaves'``
For each i, ``H[i] == j``, cluster node ``j`` appears in position
``i`` in the left-to-right traversal of the leaves, where
:math:`j < 2n-1` and :math:`i < n`. If ``j`` is less than ``n``, the
``i``-th leaf node corresponds to an original observation.
Otherwise, it corresponds to a non-singleton cluster.
``'leaves_color_list'``
A list of color names. The k'th element represents the color of the
k'th leaf.
See Also
--------
linkage, set_link_color_palette
Notes
-----
It is expected that the distances in ``Z[:,2]`` be monotonic, otherwise
crossings appear in the dendrogram.
Examples
--------
>>> import numpy as np
>>> from scipy.cluster import hierarchy
>>> import matplotlib.pyplot as plt
A very basic example:
>>> ytdist = np.array([662., 877., 255., 412., 996., 295., 468., 268.,
... 400., 754., 564., 138., 219., 869., 669.])
>>> Z = hierarchy.linkage(ytdist, 'single')
>>> plt.figure()
>>> dn = hierarchy.dendrogram(Z)
Now, plot in given axes, improve the color scheme and use both vertical and
horizontal orientations:
>>> hierarchy.set_link_color_palette(['m', 'c', 'y', 'k'])
>>> fig, axes = plt.subplots(1, 2, figsize=(8, 3))
>>> dn1 = hierarchy.dendrogram(Z, ax=axes[0], above_threshold_color='y',
... orientation='top')
>>> dn2 = hierarchy.dendrogram(Z, ax=axes[1],
... above_threshold_color='#bcbddc',
... orientation='right')
>>> hierarchy.set_link_color_palette(None) # reset to default after use
>>> plt.show()
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