With respect to what?: Simultaneous interaction with dimension reduction and clustering projections

Direct manipulation interactions on projections are often incorporated in visual analytics applications. These interactions enable analysts to provide incremental feedback to the system in a semi-supervised manner, demonstrating relationships that the analyst wishes to find within the data. However, determining the precise intent of the analyst is a challenge. When an analyst interacts with a projection, the inherent ambiguity of some interactions leads to a variety of possible interpretations that the system could infer. Previous work has demonstrated the utility of clusters as an interaction target to address this "With Respect to What" problem in dimension-reduced projections. However, the introduction of clusters introduces interaction inference challenges as well. In this work, we discuss the interaction space for the simultaneous use of semi-supervised dimension reduction and clustering algorithms. Within this exploration, we highlight existing interaction challenges of such interactive analytical systems, describe the benefits and drawbacks of introducing clustering, and demonstrate a set of interactions from this space.