Can a classifier  be used to measure the Clustering Quality measure?

I have come across this paper where the researcher uses a classifier  like :  five nearest neighbor classifier, a C4.5 decision tree, and a Rocchio classifier .

But I'm not sure how these classifiers help in the Measuring the clustering quality of a dataset. Can anyone explain how the different classifiers  help in the Measuring the clustering quality of a dataset?

The paper says in section 3 that "The basis of our new CQM is the notion

that clustering’s purpose is the unsupervised prediction of

behavior from populations. While prediction suggests some

form of classification, there are typically no labels during

clustering, preventing classification’s use. However, in the

context of a CQM, which is computed after a clustering

is complete, we do in-fact have a labeling that a classifier

can use—the clustering itself."

Could not understand 

https://bitbucket.org/parashararamsees/clustering-quality-measure/downloads