Optimization and data structure: Seven faces of dual scaling

Dual scaling can be looked at as several different optimization problems, which suggests a number of optimal properties inherent in this scaling method. This study identifies some of its old and new aspects, providing a brief, but comprehensive, characterization of dual scaling. It is important to be aware of its limitations as well as possibilities, particularly because the method is deterministic or mathematical rather than probabilistic or statistical, hence rendering it a greater risk of misapplication. Seven key characteristics of dual scaling are identified and discussed.