State-of-the-art visual analytics techniques in application domains are often designed by VA professionals over qualitative requirement collected from end users. These VA techniques may not leverage users' domain knowledge about how to achieve their analytical goals. In this position paper, we propose a user-driven design process of VA applications centered around a new concept called analytical representation (AR). AR features a formal abstraction of user requirement and their desired analytical trails for certain VA application, and is independent of the actual visualization design. A conceptual graph schema is introduced to define the AR abstraction, which can be created manually or constructed by semi-automated tools. Designing VA applications with AR provides a shared opportunity for both optimal analysis blueprint from the perspective of end users and optimal visualization/algorithm from the perspective of VA designers. We demonstrate the usage of the design process in two case studies.