In many cases, it's impossible to evaluate the performance of a clustering algorithm using only a visual inspection. Moreover, it's important to use standard objective metrics that allow for comparing different approaches. We are now going to introduce some methods based on the knowledge of the ground truth (the correct assignment for each sample) and one common strategy employed when the true labels are unknown.
Before discussing the scoring functions, we need to introduce a standard notation. If there are k clusters, we define the true labels as:
In the same way, we can define the predicted labels:
Both sets can be considered ...
