scipy.cluster.hierarchy.leaders(Z, T)[source]

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

• leaf descendents belong only to flat cluster j (i.e. T[p]==j for all $$p$$ in $$S(i)$$ where $$S(i)$$ is the set of leaf ids of leaf nodes descendent with cluster node $$i$$)
• there does not exist a leaf that is not descendent with $$i$$ that also belongs to cluster $$j$$ (i.e. T[q]!=j for all $$q$$ not in $$S(i)$$). 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. 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. For example: if L=2 and M=8, the flat cluster with id 8’s leader is linkage node 2. 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.

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