scipy.cluster.hierarchy.optimal_leaf_ordering(Z, y, metric='euclidean')[source]#

Given a linkage matrix Z and distance, reorder the cut tree.


The hierarchical clustering encoded as a linkage matrix. See linkage for more information on the return structure and algorithm.


The condensed distance matrix from which Z was generated. Alternatively, a collection of m observation vectors in n dimensions may be passed as an m by n array.

metricstr or function, optional

The distance metric to use in the case that y is a collection of observation vectors; ignored otherwise. See the pdist function for a list of valid distance metrics. A custom distance function can also be used.


A copy of the linkage matrix Z, reordered to minimize the distance between adjacent leaves.


>>> import numpy as np
>>> from scipy.cluster import hierarchy
>>> rng = np.random.default_rng()
>>> X = rng.standard_normal((10, 10))
>>> Z = hierarchy.ward(X)
>>> hierarchy.leaves_list(Z)
array([0, 3, 1, 9, 2, 5, 7, 4, 6, 8], dtype=int32)
>>> hierarchy.leaves_list(hierarchy.optimal_leaf_ordering(Z, X))
array([3, 0, 2, 5, 7, 4, 8, 6, 9, 1], dtype=int32)