Hands-On Unsupervised Learning with Python

Completeness score

This measure (together with all the other ones discussed from now on) is based on knowledge of the ground truth. Before introducing the index, it's helpful to define some common values. If we denote with Y_true the set containing the true assignments and with Y_pred, the set of predictions (both containing M values and K clusters), we can estimate the following probabilities:

In the previous formulas, n_true/pred(k) represents the number of true/predicted samples belonging the cluster k ∈ K. At this point, we can compute the entropies of Y_true and Y_pred:

Considering the definition of entropy, H(•) is maximized by a uniform ...