3.1.3.3. scipy.cluster.hierarchy.leaders¶

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

Returns 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.