What is the rationale, if any, to use Discriminant Analysis (DA) on the results of a clustering algorithm like k-means, as I see it from time to time in the literature (essentially on clinical subtyping of mental disorders)?
It is generally not recommended to test for group differences on the variables that were used during cluster construction since they support the maximisation (resp. minimisation) of between-class (resp. within-class) inertia. So, I am not sure to fully appreciate the added value of predictive DA, unless we seek to embed individuals in a factorial space of lower dimension and get an idea of the "generalizability" of such a partition. But even in this case, cluster analysis remains fundamentally an exploratory tool, so using class membership computed this way to further derive a scoring rule seems strange at first sight.
Any recommendations, ideas or pointers to relevant papers?