Evaluation methods based on the ground truth

In this section, we present some evaluation methods that require the knowledge of the ground truth. This condition is not always easy to obtain because clustering is normally applied as an unsupervised method; however, in some cases, the training set has been manually (or automatically) labeled, and it's useful to evaluate a model before predicting the clusters of new samples.

Homogeneity

An important requirement for a clustering algorithm (given the ground truth) is that each cluster should contain only samples belonging to a single class. In Chapter 2, Important Elements in Machine Learning, we have defined the concepts of entropy H(X) and conditional entropy H(X|Y), which measures the uncertainty of X given the knowledge of Y. Therefore, if the class set is denoted as C and the cluster set as K, H(C|K) is a measure of the uncertainty in determining the right class after having clustered the dataset. To have a homogeneity score, it's necessary...