Artificial Intelligence (AI) has been on the rise in many domains, including numerous safety-critical applications. However, for complex systems in the real world, defining the underlying environmental conditions in which the AI-based system must operate -- the Operational Design Domain (ODD) -- is extremely challenging. This often results in an incomplete description of the ODD, which contrasts with the requirements of many domains for certifying AI-based systems. Traditionally, the ODD is created in the early stages of the development process, drawing on sophisticated expert knowledge and related standards. This paper presents a novel Safety-by-Design method to a posteriori define the ODD from previously collected data using a multi-dimensional kernel-based representation. This approach is validated through both Monte Carlo methods and a real-world aviation use case for a future collision-avoidance system. Moreover, by defining under what conditions two ODDs are similar, the paper shows that the data-driven ODD can produce a dataset similar to the original, hidden ODD. Deriving the novel, Safety-by-Design, deterministic kernel-based affinity representation of ODDs is fully automated via a bounded, order-independent algorithm. Utilizing the proposed ODD representation enables future certification of data-driven, safety-critical AI-based systems.