cluster_hill_number#
- er_evaluation.cluster_hill_number(membership, alpha=1)[source]#
Compute Hill number of a given order.
- Hill numbers:
The Hill number of order \(\alpha \geq 0\) of a given probability distribution \(p_i\), \(i =0,1,2, \dots\), is defined as
\[H_\alpha = \left(\sum_{i} p_i^{\alpha} \right)^{1/(1-\alpha)}\]and continually extended at \(\alpha =0, 1\). Here, we let \(p_i\) be the proportion of clusters of size \(i\).
- Parameters:
membership (Series) – Membership vector representation of a clustering.
alpha (int, optional) – Order of the Hill Number. Defaults to 1.
- Returns:
Hill number of order alpha for the given clustering.
- Return type:
float
Examples
>>> membership = pd.Series(index=[1,2,3,4,5,6,7,8], data=[1,1,2,3,2,4,4,4]) >>> cluster_hill_number(membership, alpha=0) 3
>>> cluster_hill_number(membership, alpha=1) 2.82842712474619
>>> cluster_hill_number(membership, alpha=np.Inf) 2.0