There are two types of validation in clustering, using:
Internal indexes: Used to measure the goodness of a clustering structure without respect to external information (e.g., sum of squared errors)
External indexes: Consists in comparing the results of a cluster analysis to an externally known result, such as externally provided class labels (e.g., Rand index, purity, etc.)
I'm confused on the use of external validation indexes in clustering. Since the class labels are known, why use clustering (i.e., unsupervised learning) instead of supervised learning (e.g., SVM, etc.)?