Quadratic discriminant scoring for selecting clustering solutions

Selecting an optimal clustering solutions is a difficult problem. There exist many data-driven validation strategies in the literature to perform this task. In this paper, we focus on a recent proposal, based on quadratic discriminant scores and bootstrap resampling, namely the BQH and BQS from Coraggio and Coretto [4]. These strategies proved to be extremely successful with elliptic-symmetric clusters and, in general, when clusters can be separated by quadratic boundaries. In this work, we review the BQH and BQS strategies, and try to shed more light on their functioning, by comparing them with alternative likelihood-based validation indexes, and with different resampling schemes.