SciPy

scipy.cluster.hierarchy.leaders

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.

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.

For example: if L[3]=2 and M[3]=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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