Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the diagnosis group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the diagnosis to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.
The sharp Lipschitz constants for feasible and optimal solutions of a perturbed linear program
